![]() ![]() Property information displayed is deemed reliable but is not guaranteed.Ĭopyright 2023 Bright MLS, Inc. When checking Airbnb it seems like you can rent for about 150-200 and checking investment sites it seems like most pocono houses are inhabited from renters for about 75. The house is a short 50 feet from the dock where you can watch the sunrise while enjoying your morning. We are looking in Arrowhead lakes community about 5 minutes to the beach and the house is lowly priced around 100k. Some properties which appear for sale on the website may no longer be available because they are for instance, under contract, sold or are no longer being offered for sale. Its perfect for romantic getaways or family vacations. The property information being provided on or through the website is for the personal, non-commercial use of consumers and such information may not be used for any purpose other than to identify prospective properties consumers may be interested in purchasing. Listing information is from various brokers who participate in the Bright MLS IDX program and not all listings may be visible on the site. The data relating to real estate for sale on this website appears in part through the BRIGHT Internet Data Exchange program, a voluntary cooperative exchange of property listing data between licensed real estate brokerage firms, and is provided by BRIGHT through a licensing agreement. Consult the specific municipality for permitted Zoning uses. ![]() Information is for consumer’s personal noncommercial use, and may not be used for any purpose other than identifying properties which consumers may be interested in purchasing. Information provided by the Greater Scranton Board of REALTORS® MLS. The listing broker’s offer of compensation is made only to participants of the MLS where the listing is filed. The information contained herein is believed to be accurate, but no warranty as such is expressed or implied. Explore the homes with Waterfront that are currently for sale in Pocono Lake, PA, where the average value of homes with Waterfront is 266,950. All listing data is the copyrighted property of the aforesaid Associations and its MLS-IDX Participants with all rights reserved. Listings marked with the Internet Data Exchange logo are not necessarilty the listings of the owner of this web site. The data relating to real estate for sale on this web site includes listings held by MLS-IDX Participants of the Internet Data Exchange program of the Multiple Listing Service of the Pocono Mountains Association of Realtors®. ![]()
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![]() It is an ideal choice for entry-level collectors or those looking for an affordable, yet reliable Katana.ġ060 Carbon Steel: With a 0.60% carbon content, 1060 Carbon Steel strikes a balance between durability and flexibility. The steel types we offer include:ġ045 Carbon Steel: Containing 0.45% carbon, 1045 Carbon Steel is a tough and durable option that offers excellent value for money. Our selection ensures that you can find the perfect sword to match your requirements and budget. The sword's design allowed for swift, powerful cuts and thrusts, making it a formidable weapon in the hands of a skilled samurai.Īt Mini Katana, we celebrate the rich history and craftsmanship of the Katana, offering a range of expertly crafted swords and replicas for enthusiasts, collectors, and those who appreciate the art of traditional Japanese sword-making. Katanas were employed in various battle scenarios, from one-on-one duels to larger-scale skirmishes and battles. Samurai warriors would often carry their Katana alongside a smaller sword, such as a Wakizashi or Tanto, as part of a Daisho – a matched pair of swords symbolizing their social status and warrior spirit. The Katana became the primary weapon of the samurai during the late Kamakura period (1185-1333) and continued to be used in subsequent periods, such as the Muromachi (1336-1573) and Edo (1603-1868) periods. These iconic swords, characterized by their curved, single-edged blade, were primarily designed for cutting and were particularly effective in close-quarters combat. Yes, Katanas were indeed used in battle by samurai warriors throughout Japanese history. Other swords have their unique cultural and historical significance, depending on the region and time period in which they were used.Īt Mini Katana, we celebrate the beauty and craftsmanship of traditional Japanese Katanas, offering a range of expertly made swords and replicas for collectors and enthusiasts alike. They are not only weapons but also symbols of social status, honor, and craftsmanship. ![]() Historical and Cultural Context: Katanas hold a special place in Japanese history and culture, being the primary weapon of the samurai warrior class. In comparison, other swords may have various grip and guard designs, depending on their origin and intended use. The guard, or Tsuba, is usually round or square and features intricate designs that reflect the culture and artistry of Japan. This allows for greater control and power when wielding the sword. Grip and Guard: Katanas have a long handle, typically wrapped in a traditional Japanese style with cord or leather, designed to accommodate a two-handed grip. Other swords may be forged using different techniques and materials, depending on the region and time period in which they were made. ![]() This process results in a strong, sharp, and resilient weapon. In contrast, other swords, such as European longswords, may have straight, double-edged blades that are suited for both cutting and thrusting.Ĭonstruction: Katanas are crafted using traditional Japanese forging techniques, which involve folding and differentially heat-treating the steel to create a blade with a harder cutting edge and a softer, more flexible spine. The curvature of the blade allows for more effective slashing motions and improves the sword's overall cutting ability. Here are some key differences between a Katana and other swords:īlade Shape: Katanas have a distinct, curved, single-edged blade, which is designed primarily for cutting. ![]() A "Katana," on the other hand, refers specifically to a traditional Japanese sword, characterized by its unique features and design. The term "sword" is a general term that encompasses a wide variety of bladed weapons used across different cultures and historical periods. ![]() ![]() ![]() It may be a good idea to search for higher or lower backing tracks if the original key doesn’t sit well with your voice. In the key of C# minor, this song explores a lower range of the voice. This rap is a good alternative to the typical pop songs that you may choose to sing at a talent show. Some have pretty positive messages to give. With the lead singer of this song having a distinct voice, you shouldn’t try and directly mimic her style- always make it your own. This fun song could be the perfect opportunity to show off some energetic dance moves, really honing your performance technique and audience engagement at a competition. Family friendly songs #1 Dance Monkey by Tones and I It’s easy to fall into a trap of wanting to sing a pop song that you like the sound of but has inappropriate lyrics.Ī good example of age-appropriate pop songs with clean lyrics that you can draw inspiration from, are the compilation albums from Kidz Bop. ![]() A child’s love for a pop song is usually nothing to do with their relationship to the lyrics, but instead the melody of the song. It’s harder to connect with your audience and display emotion through lyrics (skills that a competition judging panel would be looking for) if you can’t relate to the songs subject matter. You can see this age as an exciting time to transition from basic kid-friendly classics to clean versions of chart hits. At this stage, you’re not quite in the teen category but you also don’t want to be singing ‘babyish’ songs. Clean songs with clean lyrics for kids to singĬhildren between the ages of 9-12 are more likely to struggle to find age-appropriate songs. If you’re in a singing competition, or you are looking to apply for one, then choosing a song to sing with clean lyrics is as equally as important as choosing a song that shows off your vocal ability. So, before searching for the lyrics of your favourite song you’ve heard on the radio, it’s a good idea to make sure you look for the clean song version. A lot of the music that you hear on radio stations has undergone ‘clean editing’, basically meaning that the lyrics won’t match the ones on the original recordings. It’s important to make sure you choose so-called ‘clean songs’ that not only match your vocal ability but also deliver an age-appropriate message through lyrics. Some songs can use swear words, or may contain sexist, violent or racist material, which can also be inappropriate. You’re never too old to start singing, but sometimes songs that are popular in the charts may not be age-appropriate. So, what are some good songs to sing with clean lyrics and what are the best age-appropriate songs for kids to perform? Whether you’re looking for a perfect talent show number with clean lyrics or a hit to sing along to in your bedroom, this article gives you some of the best suggestions.Īre you looking for age-appropriate songs to sing and do you struggle to find songs with clean lyrics? Are you looking for the right song to sing at a competition? Below we give you 29 age-appropriate songs suggestions with clean lyrics. ![]() Here are some good songs for kids for you to choose from, suitable for all ages. When you’re auditioning for a singing competition, it’s also a good idea to choose songs that have clean lyrics. To begin, each grade level will have a 30-minute session per week.If you’re a young singer, it’s important to have a range of clean songs (i.e. With many children staying home from school or school plans uncertain, we thought NOW would be an even better time to introduce this exciting new program. We will begin a virtual six-week session, LIVE taught by one of our Starpath teachers, for each elementary grade level K-3. This program has been in the works for years and was scheduled to become a reality this fall with the opening of our new Green Level West location. Curriculum Standards and will focus on literacy, mathematics and science, and learning grade-specific concepts through dance - moving, reading, choreographing and more. Miss Lindsey created the Professor Pirouette program to engage children in academics through dance! This program follows N.C. ![]() ![]() ![]() Get Answers Right From Your Android or iPhone.Bust A Cheating Partner Without Them Knowing.But before we go over our top pick in detail, let’s check out the entire list of the 6 best car tracking devices with no monthly fees! LandAirSea GPS – #1 Pick For Best No Subscription Fee GPS Car Tracker And what product tops our list as the best no monthly GPS tracker? The answer is a device called LandAirSea GPS. It’s about getting you value, cutting through the noise, and delivering the goods. We’re talking real-time updates, no hidden costs, and a device that doesn’t just meet, but crushes your expectations. You want a GPS tracker, no monthly fee? Well, you’re in the right spot! This isn’t just some humdrum guide, it’s THE roadmap to finding thee best vehicle tracking device with no subscription fees. Do All GPS Trackers Have A Monthly Fee? What Is The Best Car Tracking Device With No Monthly Fee?.How Many Satellites Are Used In GPS 2023?.Top 5 Reasons To Use A No Monthly Fee GPS Tracker. ![]() How Does Passive GPS Work: A Step-By-Step Explanation.What Is A No Monthly Fee GPS Tracking Device?.GPS Tracker No Monthly Fee – What Buyer’s Should Look For Before Purchasing.Invoxia Real Time GPS Tracker – FREE 2 Year Subscription.LandAirSea Sync – No Subscription GPS With Fastest Updates.GPSit 1000BZL LTE Vehicle Tracking Device.LandAirSea GPS Tracking Key – #1 GPS Data Logger Of All-Time.Vyncs Premium – Best OBD 4G LTE On Amazon.LandAirSea GPS – #1 Pick For Best No Subscription Fee GPS Car Tracker.What Is The Best Car Tracking Device With No Monthly Fee?. ![]() ![]() Flamingos filter-feed on shellfish and algae. Order: Phoenicopteriformes Family: Phoenicopteridaeįlamingos are gregarious wading birds, usually 3 to 5 feet (0.9 to 1.5 m) tall, found in both the Western and eastern Hemispheres. Ring-necked pheasant, Phasianus colchicus (I).In general, they are plump (although they vary in size) and have broad, relatively short wings. The Phasianidae are a family of terrestrial birds. White-headed duck, Oxyura leucocephala (A) (endangered).Red-breasted merganser, Mergus serrator.Hooded merganser, Lophodytes cucullatus (A).Long-tailed duck, Clangula hyemalis (vulnerable).Black scoter, Melanitta americana (A) (near-threatened).White-winged scoter, Melanitta deglandi (A).Velvet scoter, Melanitta fusca (vulnerable).Surf scoter, Melanitta perspicillata (A).Harlequin duck, Histrionicus histrionicus (A).Common eider, Somateria mollissima (near-threatened).Steller's eider, Polysticta stelleri (A) (vulnerable).Ferruginous duck, Aythya nyroca (near-threatened).Common pochard, Aythya ferina (vulnerable).Marbled teal, Marmaronetta angustirostris (A) (vulnerable).Falcated duck, Mareca falcata (A) (near-threatened).Egyptian goose, Alopochen aegyptiacus (I).Red-breasted goose, Branta ruficollis (A) (vulnerable).Pink-footed goose, Anser brachyrhynchus.Lesser white-fronted goose, Anser erythropus (vulnerable).Greater white-fronted goose, Anser albifrons.(B) Before 1800 - species "recorded only before 1800 (location and/or date not well enough documented)" per the CDNA.(I) Introduced - a species whose "ancestors originated from captivity or ship transport" and which have been established for at least 20 years per the CDNA.(A) Accidental - a species that rarely or accidentally occurs in the Netherlands, requiring review by the CDNA for inclusion in the record.The notes of population status such as "endangered" apply to the world population and are from Bird Checklists of the World. ![]() The following tags have been used to highlight some categories of occurrence. This list's taxonomic treatment (designation and sequence of orders, families and species) and nomenclature (English and scientific names) are those of The Clements Checklist of Birds of the World, 2022 edition. Two species were inadequately documented before 1800. Of these species, 13 have been introduced by humans, and one is extinct. The checklist "incorporates all decisions by the Dutch rarities committee 'Commissie Dwaalgasten Nederlandse Avifauna' (CDNA) and the Dutch taxonomic committee 'Commissie Systematiek Nederlandse Avifauna' (CSNA)". The avifauna of the Netherlands included a total of 564 species documented in the wild through October 2022 according to Checklist of Dutch Bird Species with supplemental additions from Avibase. ![]() This is a list of the bird species recorded in the Netherlands. ![]() ![]() After the battle, the so-called Earth Space Defense was established, with Area 51 becoming its headquarters. Usher), son of Steven Hiller, who died in the years since the battle. She's friends with Dylan Dubrow-Hiller (Jessie T. Patty was a pilot for the military, but she resigned to take care of her father, as he is more frail and disturbed after the invasion. Whitmore's daughter, Patricia (Maika Monroe), works for current president Elizabeth Lanford (Sela Ward). The creature growls, but it's just a nightmare that Whitmore wakes up from in a jolt. A creature is observing Thomas Whitmore's (Bill Pullman) rousing speech during the battle that took place 20 years earlier (from the first Independence Day film). story opens in outer space on the alien mothership. Whitmore arrives and along with Okun and the African, they compare notes and they deduce why the aliens came to Earth 20 years ago. Levinson arrives at Area 51 and gives the thing to Okun. At the same time an alien ship like the one who attacked the planet 20 years ago shows up and attacks the planet. They go to the moon and he inspects the craft and finds something. Levinson asks Whitmore's daughter to ask her boyfriend who is among the ones at the moon base to pick him up. Levinson wants to go to the moon but the President wants him to attend the anniversary celebration. The President gives the order and shoots it down. ![]() The President is being advised to shoot it down but Levinson doesn't think they should. And sure enough a space craft appears just near the moon. Whitmore tries to warn everyone that the aliens are returning. Okun who fell into a coma 20 years after being attacked telepathically by an alien wakes up and starts drawing the same thing Whitmore is. The leader is also drawing the same things that Whitmore is. ![]() ![]() The leader who is on possession of the craft, takes Levinson and they discover they sent a distress signal before it went down and apparently it was drilling through the Earth's core. David Levinson the man who figured out how to defeat the aliens travels to Africa to inspect one of the alien ships that crashed. President Whitmore who led the attack on the aliens 20 years ago is acting strangely and is drawing some strange symbols. And just as the anniversary is approaching, strange things are happening. 20 years after defeating the aliens who invaded the Earth, the world is almost a Utopia wherein technology taken from the aliens have made the planet a paradise. ![]() ![]() ![]() Please download the NETGEAR Nighthawk App for all NETGEAR WiFi routers. I went to C:Program Files (x86)NETGEAR Geniebin and opened the Compatibility settings for NETGEARGenie.exe and told it to run in Compatibility Mode for Windows 7. Please download the NETGEAR Orbi App for all Orbi WiFi Systems. I am running Windows 8.1 and was having the same issue.WNDR3400, WNR2000 + other older router modelsįor a list of supported products, please visit here.The NETGEAR genie app is an easy way to manage, monitor, and repair your home network-from the palm of your hand. While on your home network, the NETGEAR genie app allows you to access router features with your mobile device. Securely connect smart phones and tablets to your home wireless network with a QR code thanks to EZ Mobile Connect.Stream music and video files anywhere in your network from your smartphone or tablet.Easily control your home network through the genie dashboard.You can access the following router settings using the NETGEAR genie app: wireless settings, network map, Parental Controls, guest access, traffic metering, MyMedia, and more. The NETGEAR genie app does not work if your mobile device is connected to the router’s guest network. The NETGEAR genie only works when your mobile device is connected to a NETGEAR router that is in router mode, not in access point mode. Note: In case it automatically logged in after clicking on Router Settings, you can just click on Logout to go back to the login screen. Click on Router Settings and select Remote Access for Login as. The NETGEAR genie only works when your mobile device is connected to a NETGEAR router that is in router mode, not in access point mode. Open the NETGEAR Desktop genie software on your local computer (this is the computer that’s connected to your router). The NETGEAR genie app does not work with a wireless extender or repeater. The NETGEAR genie app does not work with a wireless extender or repeater. Login with your Google Play Store account. The NETGEAR genie app currently does not support IPv6. Choose one of the app from the search result list.Then, open Google Play Store and search for NETGEAR Genie. Refer to below link for supported router list: If IPV6 is enabled, logging in to the router using the genie app will fail. ![]() My network is a 1st rev Netgear WNDR 3700 with a WN3000RP network extender. I am running an iPhone 6S with iOS 12.1.3 and my app just loaded and logged into my network in about 8 seconds. ![]() ![]() This is a top pick for a specimen tree due to its four-season interest: The Royal Raindrops Crabapple is a specialty flowering crabapple tree known for its bright magenta-pink flowers, purple leaves, and large upright form. The fruit is also very attractive to small songbirds like chickadees. While these tiny crabapples are too small to be eaten like an apple, they are still edible and can be used to make jelly. Sargent Crabapple fruits are dark red pea-sized crabapples. This type is also known for its fragrant white flowers that open from rosy pink buds. This variety is popular due to its natural dwarf size, with mature trees usually growing to a maximum of ten feet tall. For questions and advice, contact the Extension's Horticulture Help Desk at 92.The Sargent Crabapple is perhaps the most popular type of crabapple tree around. Vijai Pandian is horticultural agent/educator for Brown County University of Wisconsin-Extension. Molazam (Molten Lava): broadly weeping form, 14 feet tall, 20 feet wide, white flowers, bright red fruit. Manbeck Weeper (Anne E.): wide-spreading, horizontal weeper, 10-12 feet tall, 10-12 feet wide, white flowers, cherry-red fruit, persistent fruit, is difficult to find, but is one of the nicest crabs. Louisa: graceful weeper, 15 feet tall, 15 feet wide, pink flowers, fruit are yellow turning orange-brown, not showy or persistent. Weeping formĬoral Cascade: semi-weeping form, 15 feet tall, 20 feet wide, white flowers, coral fruit, persistent fruit. Prairie Maid: rounded to spreading form, 20 feet tall, 25 feet wide, burgundy-tinged leaves in spring, but is a watersprouter. Prairifire: upright, spreading to rounded form, 20 feet tall, 20 feet wide, slower growing, purple leaves become reddish-green. JFS-KW5 ( Royal Raindrops): upright, spreading form, 20 feet tall, 15 feet wide, cutleaf, purple leaves, orange-red fall color, persistent fruit. Malus sargentii Candymint :low, spreading, horizontal form, 10 feet tall, 15 feet wide, purple-tinted foliage becoming bronze-green. Pink or reddish flowers/red to purplish-red fruit Ormiston Roy: broad, rounded form, 20-25 feet tall, 25 feet wide, furrowed, orangish bark, yellow fruit with a rosy blush turn orange-brown after a hard frost. Lanzam (Lancelot): compact, upright, dense form, 8-10 feet tall, 8 feet wide, persistent fruit. White flowers/yellow fruitĬinzam (Cinderella): dwarf, rounded to upright form, 8 feet tall, 5 feet wide, persistent fruit.Įxcazam (Excalibur): upright form, 10 feet tall, 8-10 feet wide, good form. Tina: small, rounded, dwarf form, 5 feet tall, 6 feet wide, slow growing. Select A (Firebird): rounded, spreading form, 7 feet tall, 9 feet wide, persistent fruit, bears annually. Malus sargentii: Sargent crabapple, low, spreading form, 8 feet tall, 12 feet wide, alternate bearing, persistent fruit. Malus baccata: Jackii crabapple, hardy to zone 3, rounded form, 20 feet tall, 20 feet wide, glossy leaves. Sutyzam (Sugar Tyme): upright, spreading, oval form, 18 feet tall, 15 feet wide, persistent fruit. If you dislike the fruits of crabapples, consider a fruitless cultivar like ‘Spring Snow,’ but it is susceptible to scab disease.įollowing is the list of disease-resistant flowering crabapple cultivars referenced from UW-Extension fact sheet “Top Ornamental Crabapples for Wisconsin”: White flowers/red fruitĪdirondack: narrow, upright form, 18 feet tall, 10 feet wide, persistent fruit. Other desirable characteristics to take into consideration are the persistent small size fruits and the shape of its canopy (weeping, upright, oval, columnar, pyramidal). ![]() Some of the cultivars like Profusion, Snowdrift, Red Jade, Red Baron, Prairie, Harvest Gold and Birdland are highly susceptible to scab disease that causes significant leaf drop during the summer. When selecting a crabapple, always choose scab-resistant cultivars. ![]() ![]() ![]() Travel through traffic signal and across Rental Car Center bridge. Traveling southbound on I-85: Take Airport Blvd./Camp Creek Parkway exit (exit 72). ![]() Check the Fastbreak monitor for your name. If you’re a Budget Fastbreak member, bypass the rental counter – just walk straight ahead past Budget on your left, then turn right to walk over the outdoor bridge to the garage. Proceed down the escalator, following signs for Budget. Listen for the announcement for Rental Car Center and get off. The ATL Skytrain will arrive within 2-3 minutes – hop on. Take the escalator or elevator to the second floor. Walk outside and directly across the street to the building with glass windows. Simply get off your plane, proceed to Ground Transportation and follow signs for Rental Car Center. Nicer People, Nicer Carsĭirections for Customers Flying into Atlanta Hartsfield-Jackson International Airport: Our vehicles have more features, more fully loaded options, and tend to be newer with fewer miles on them than the competition. Welcome to Atlanta! Flying into Hartsfield–Jackson Atlanta International Airport? Need a rental car? Budget Car and Truck Rental of Atlanta has the best value in car rental with great rates on a wide variety of popular new cars, trucks, and vans. AirportĬonsolidated Rental Car Facility (CONRAC) “With a long history of profitability and appeal to a wide variety of demand segments including business and leisure, these assets will continue to benefit from the strong demand growth arising from the evolution of Sydney’s west.Budget Car and Truck Rental of Atlanta – Atlanta Hartsfield Intl. Mr Gibson added, “Complementing the remarkable growth that this region has witnessed over the last decade, the development of the new airport and Aerotropolis is anticipated to have a significant positive impact on these hotels." Western Sydney Airport and several public and private developments are being added to the existing infrastructure to support the development of the Aerotropolis. The region is experiencing a large proportion of Australia’s population growth and has positioned itself as the third largest economy in Australia behind the Sydney and Melbourne CBDs. The greater Western Sydney region is being established as a polycentric city with the development of the airport-centred Aerotropolis complemented by the strength of the existing centres of Liverpool, Greater Penrith and Campbelltown-Macarthur. “This is an exceptional opportunity allowing an in-coming purchaser to acquire two profitable and well-positioned freehold going concern hotels that offer the flexibility of vacant possession or new management, product repositioning and future redevelopment,” Mr Simpson said. The hotels are being offered for sale as a portfolio or individually and offer the option of vacant possession. Together, the hotels offer 146 economy rooms, representing a combination of a well-established, highly profitable, income-generating business with substantial freehold land holdings. Managed by Accor, Ibis Budget is recognised globally as an economy hotel brand which offers consistent quality and value-for-money accommodation and services. The hotel was refurbished in 2011 and offers 72 rooms. Ibis Budget Campbelltown, located at 3 Rennie Road in Sydney's south-west, is close to the Campbelltown town centre, train station, major road connections and key demand generators, such as Western Sydney University, TAFE NSW, Campbelltown Hospital, and Campbelltown Sports Stadium. The hotel underwent substantial renovations in 2016 and features 74 modern, well-appointed rooms. Located at 437 Hume Highway, the Ibis Budget Casula Liverpool is just over half an hour’s drive from the Sydney CBD and five minutes from Liverpool city centre. CBRE Hotel’s Michael Simpson, Tom Gibson and Vasso Zographou are managing the sale via an Expression of Interest campaign closing 31 August 2023. ![]() ![]() ![]() I get a value of 5,510,008 for that solution. (Speaking of which, Hardmath123 quoted an objective value of 5,499,341 and posted a layout. That's a bit worse than the solution Hardmath123 got in the original post. After five minutes, the incumbent solution had objective value 5,706,873. At any rate, I did the five minute run with MIP emphasis 2, which emphasizes proving optimality. Someday maybe I'll figure out why it's ignoring those carefully defined SOS1 weights. It did that even if skipped the branching priorities, which irks me a bit. I included both the branching priorities and the SOS1 constraints, but the CPLEX presolver eliminated all the SOS1 constraints as "redundant". How does this model do? I ran it for five minutes on a decent desktop PC (using four threads). The starting point for all the math programming formulations is a matrix of binary variables $x_.$$ So I'll start by discussing a couple of mixed integer linear program formulations. I'll in fact try out a quadratic model subsequently, but my inclination is always to try to linearize anything that can't outrun or outfight me. As I noted there, Nate Brixius correctly characterized the problem as a quadratic assignment problem (QAP). There 3! ways to choose the order.This continues my previous post about the problem of optimally laying out a one-dimensional typewriter keyboard, where "optimally" is taken to mean minimizing the expected amount of lateral movement to type a few selected books. Solution: From part (d) there are 24 ways to select a blue, red, and greenīook if the order does not matter. Order in which the books are selected matters? ![]() (e) In how many ways can you select 3 books, one of each color, if the The total number of arrangements is 4 ⋅ 3 ⋅ 2 = 24. Solution: There are 4 choices for the blue book, 3 for the green book, andĢ for the red book. The order in which the books are selected does not matter? (d) In how many ways can you select 3 books, one of each color, if Solution: By the multiplication principle, there will be 6 ⋅ 3 ⋅ 2 = 36ĭifferent home types available. How many different types of homes are available if a builder offers a choice ofĦ basic plans,3 roof styles,and 2 exterior finishes? Evaluate the permutation of P(13,2) Solution: 156 11! 13. But since the pairs of each color are identical, the number of distinguishable selections is 2522520 4!5!3! 2! 14! Were distinguishable there would be 14! possible selections for the next Solution: The student has 4 + 5 + 3 + 2 = 14 pairs of socks, so if the pairs In how many ways can he select socks to wear for the next two weeks? Socks,3 pairs of identical black socks, and 2 pairs of identical white socks. A student has 4 pairs of identical blue socks, 5 pairs of identical brown In how many ways can the letters in the word Mississippi be arranged? Thus the number of possible arrangements is 3780 1!4!2! 2! 9! Solution: The word Tennessee contains 9 letters, consisting of 1 t, 4 e’s, 2 n’s andĢ s’. In how many ways can the letters in the word Tennessee be arranged? If we use 3 of the 6, the number of permutations is 6. Find the number of permutations of the letters L,M,N,O,P and Q, if just three of ,then the number of distinguishable permutations is ! !.! ! n 1 n 2 nr n , pk are of kth kind and the rest, if any, are ofĭifferent kind is ! !.! ! p 1 p 2 pk n If P ( n,r) where r n, is the number of permutations of n elements taken r at a time ,then ( )! ! (, ) n r n P n r The number of permutations of a set with n elements is n ! i P( n,n)n! If the n objects in a permutation are not all distinguishable-that is ,if there are n 1 of type 1, n 2 of type 2 and so on for r different types ♦The number of permutations of n objects, where p1 objects are of one kind, Same kind and rest are all different= ! ! p n ♦The number of permutations of n objects, where p objects are of the So the number of possible arrangements isįactorial notation : The notation n! represents the product of first n natural Solution The teacher has 8 ways to fill the first space (say the one on the left), 7Ĭhoices for the next book, and so on, leaving 4 choices for the last book on the A teacher wishes to place 5 out of 8 different books on her shelf many If no digit is repeated, there are 10 choices for the first place, 9 for the second, 8įor the third, and 7 for the fourth, so there are 10 ⋅ 9 ⋅ 8 ⋅ 7 = 5040 possible Solution: Each of the four digits can be one of the ten digits 0,1, 2.,10, so thereĪre 10 ⋅ 10 ⋅ 10 ⋅ 10 or 10,000 possible sequences. Sequences are possible? How many sequences are possible if no digit is repeated. ![]() A combination lock can be set to open to any 4-digit sequence. ![]() |
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