[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-274731-105":59,"doc-detail-274731-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","permutations-and-combinations","Permutations and Combinations","","Permutations and Combinations provides a structured overview of counting methods used when order matters or doesn’t, and when repetition is allowed or not. The material defines the variables n and r, then applies the relevant permutation or combination formulas to practical scenarios such as counting codes with repeated digits, ordering balls from a pool without repetition, and forming ice-cream scoop selections where flavors may repeat. Additional examples demonstrate committee selection, password construction with mixed letter and digit rules, and arranging multiple volumes using factorial reasoning.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/permutations-and-combinations/274731/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/permutations-and-combinations/274731.png","ImageObject",300,407,{"name":92,"@type":93},"WPS_1786070896","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What do n and r represent in permutations and combinations problems?","Question",{"text":113,"@type":114},"n is the number of things available to choose from, and r is the number of things selected.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"When should you use a permutation formula versus a combination formula?",{"text":118,"@type":114},"Use permutations when order matters, and combinations when order doesn’t matter.",{"name":120,"@type":111,"acceptedAnswer":121},"How do repetition rules change the counting method?",{"text":122,"@type":114},"If repetition is allowed, use the formulas labeled with repetition; if repetition is not allowed, use the ones labeled without repetition.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},274731,1789482389,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":24},549768072016,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Permutations and Combinations  \n\n| Type | Formulas | Explanation of Variables | Example |\n| --- | --- | --- | --- |\n| Permutation with repetition\u003Cbr>(Use permutation formulas when order matters in the problem.) |  | Where n is the number of things to choose from, and you choose r of them. | A lock has a 5 digit code. Each digit is chosen from 0-9, and a digit can be repeated. How many different codes can you have?\u003Cbr>n = 10, r = 5\u003Cbr>105 = 100,000 codes |\n| Permutation without repetition\u003Cbr>(Use permutation formulas when order matters in the problem.) | ( ) | Where n is the number of things to choose from, and you choose r of them. Sometimes you can see the following notation for the same concept:\u003Cbr>| How many ways can you order 3 out of 16 different pool balls?\u003Cbr>n = 16, r = 3\u003Cbr>( ) |\n| Combination with repetition\u003Cbr>(Use combination formulas when order doesn’t matter in the problem.) | ( ) \u003Cbr>( ) | Where n is the number of things to choose from, and you choose r of them. | If there are 5 flavors of ice cream and you can have 3 scoops of ice cream, how many combinations can you have? You can repeat flavors.\u003Cbr>n = 5, r = 3\u003Cbr>( )\u003Cbr>( ) |\n| Combination without repetition\u003Cbr>(Use combination formulas when order doesn’t matter in the problem.) | ( ) | Where n is the number of things to choose from, and you choose r of them. Sometimes you can see the following notation for the same concept:\u003Cbr>| The state lottery chooses 6 different numbers between 1 and 50 to determine the winning numbers. How many combinations are possible?\u003Cbr>n = 50, r = 6\u003Cbr>( ) |\n\nPermutations and Combinations  \nExamples  \n1) Mr. Smith is the chair of a committee. How many ways can a committee of 4 be chosen from 9 people given that Mr. Smith must be one of the people selected?  \nMr. Smith is already chosen, so we need to choose another 3 from 8 people. In choosing a committee, order doesn't matter, so we need the combination without repetition formula.  \n( ) = ( ) = 56 ways  \n2) A certain password consists of 3 different letters of the alphabet where each letter is used only once. How many different possible passwords are there?  \nOrder does matter in a password, and the problem specifies that you cannot repeat letters. So, you need a permutations without repetitions formula. The number of permutations of 3 letters chosen from 26 is  \n( ) = ( ) = 15,600 passwords  \n3) A password consists of 3 letters of the alphabet followed by 3 digits chosen from 0 to 9. Repeats are allowed. How many different possible passwords are there?  \nOrder does matter in a password, and the problem specifies that you can repeat letters. So, you need a permutations with repetitions formula.  \nThe different ways you can arrange the letters = 17,576  \nThe different ways you can arrange the digits = = 1,000  \nSo the number of possible passwords = 17,576 × 1,000 = 17,576,000 passwords  \n4) An encyclopedia has 6 volumes. In how many ways can the 6 volumes be placed on the shelf?  \nThis problem doesn’t require a formula from the chart. Imagine that there are 6 spots on the shelf. Place the volumes one by one.  \nThe first volume to be placed could go in any 1 of the 6 spots. The second volume to be placed could then go in any 1 of the 5 remaining spots, and so on. So the total number of ways the 6 volumes could be placed is  \n6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 ways  \nPermutations and Combinations","cbCaildf3LLv6IlO","https://ap.wps.com/l/cbCaildf3LLv6IlO","pdf",404469,"English","# Permutations and Combinations\n## Types of formulas (with and without repetition)\n## Examples","[{\"question\":\"What do n and r represent in permutations and combinations problems?\",\"answer\":\"n is the number of things available to choose from, and r is the number of things selected.\"},{\"question\":\"When should you use a permutation formula versus a combination formula?\",\"answer\":\"Use permutations when order matters, and combinations when order doesn’t matter.\"},{\"question\":\"How do repetition rules change the counting method?\",\"answer\":\"If repetition is allowed, use the formulas labeled with repetition; if repetition is not allowed, use the ones labeled without repetition.\"}]","Permutations and Combinations | PDF"]