[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-265105-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-265105-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","permutations-and-combinations-ged-math-quick-review","Permutations and Combinations - GED Math - Quick Review","","GED Math quick review focused on permutations and combinations, explaining factorial notation n! and the core formulas for ordered arrangements nPr=(n−r)! and selections nCr=n!/(r!(n−r)!). Includes concise guidance on choosing the correct counting rule based on whether order matters, followed by practice exercises evaluating factorial, permutation, and combination expressions. Word problems cover selecting ordered pairs and unordered toppings, forming arrangements without repeats, and counting possible teams from a group.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/permutations-and-combinations-ged-math-quick-review/265105/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/permutations-and-combinations-ged-math-quick-review/265105.png","ImageObject",300,407,{"name":42,"@type":43},"Finn","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",20,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the difference between permutations and combinations?","Question",{"text":63,"@type":64},"Permutations count arrangements where order matters, using nPr=(n−r)!. Combinations count selections where order does not matter, using nCr=n!/(r!(n−r)!).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you evaluate expressions involving factorials?",{"text":68,"@type":64},"Use factorial n! as the product of every whole number from n down to 1. Then substitute into the permutation or combination formulas when needed.",{"name":70,"@type":61,"acceptedAnswer":71},"How do the word problems determine whether to use P or C?",{"text":72,"@type":64},"If the problem says order matters (e.g., president and vice-president), use permutations. If order does not matter (e.g., choosing toppings), use combinations.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},265105,1789392406,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":55,"slug":118},9,"Religion & Spirituality","religion-spirituality",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":55,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":30,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":80,"read_time":111},34359740700684,"https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487","Practice 􀀏 Progress 􀀏 Succeed | GED Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nPermutations and Combinations  \n\n| Name:   | D | ate:   | S | core:   / 18 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nn!   \nA permutation counts arrangements where order matters: nPr = (n 􀀀 r)! . A com  \nn!  \nbination counts selections where order does not matter: nCr = ~~ ~~ . Re  \nr! (n 􀀀 r)!  \nmember that n! (factorial) means multiply every whole number from n down to 1.  \n▷ Example: In how many ways can you arrange 3 of 5 books on a shelf (order matters)? Work: Order matters, so use a permutation: 5 P3 = (5~~ ~~3)! = 52!! = 1220 . ⋆ Answer: 60  \n♦ Practice Problems  \nEvaluate each expression.  \n1. 4! 8. 6 C2  \n2. 5! 9. 7 C3  \n3. 3! 10. 4 C1  \n4. 5 P2 11. 6 P2  \n5. 6 P3 12. 5 C5  \n6. 4 P4 13. 8 C2  \n7. 5 C2 14. 7 P2  \n♦ Word Problems  \n15. In how many ways can a president and a vice-president be chosen from a club of 6 members (order matters)?  \n16. How many ways can you choose 2 toppings from 5 available toppings (order does not matter)?  \n17. How many different 3-letter arrangements can be made from the letters A, B, C, D with no repeats (order matters)?  \n18. A team of 3 is chosen from 8 players (order does not matter) . How many different teams are possible?  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | GED Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \n1. 24 7. 10 13. 28  \n2. 120 8. 15 14. 42  \n3. 6 9. 35 15. 30  \n4. 20 10. 4 16. 10  \n5.  120  11. 30 17. 24  \n6. 24 12. 1 18. 56  \nStep-by-Step Explanations  \n1. Start by naming the process: Decide whether order matters, then use the counting rule, permutation rule, or combination rule that 􀀂ts. The setup/work is A factorial multiplies down to 1: 4! = 4 􀀂 3 􀀂 2 􀀂 1 = 24 . So the 􀀂nal answer is 24.  \n2. A good way to think about this is: Decide whether order matters, then use the counting rule, permutation rule, or combination rule that 􀀂ts. The setup/work is 5! = 5 􀀂 4 􀀂 3 􀀂 2 􀀂 1 = 120 . So the 􀀂nal answer is 120.  \n3. Step by step: Decide whether order matters, then use the counting rule, permutation rule, or combination rule that 􀀂ts. The setup/work is 3! = 3 􀀂 2 􀀂 1 = 6 . So the 􀀂nal answer is 6.  \n4. Take it one move at a time: Decide whether order matters, then use the counting rule, permutation rule, or combination rule that 􀀂ts. The setup/work is Permutations count ordered choices: 5 P2 = 5 􀀂 4 = 20 . So the 􀀂nal answer is 20.  \n5. Start by naming the process: Decide whether order matters, then use the counting rule, permutation rule, or combination rule that 􀀂ts. The setup/work is 6 P3 = 6 􀀂 5 􀀂 4 = 120 . So the 􀀂nal answer is 120.  \n6. A good way to think about this is: Decide whether order matters, then use the counting rule, permutation rule, or combination rule that 􀀂ts. The ","cbCaivPTxm8hZr6x","https://ap.wps.com/l/cbCaivPTxm8hZr6x","pdf",112392,"English","# Quick Review and Helpful Hints\n## Permutation and Combination Rules\n## Practice Problems\n## Word Problems\n## Answer Keys\n## Step-by-Step Explanations","[{\"question\":\"What is the difference between permutations and combinations?\",\"answer\":\"Permutations count arrangements where order matters, using nPr=(n−r)!. Combinations count selections where order does not matter, using nCr=n!/(r!(n−r)!).\"},{\"question\":\"How do you evaluate expressions involving factorials?\",\"answer\":\"Use factorial n! as the product of every whole number from n down to 1. Then substitute into the permutation or combination formulas when needed.\"},{\"question\":\"How do the word problems determine whether to use P or C?\",\"answer\":\"If the problem says order matters (e.g., president and vice-president), use permutations. If order does not matter (e.g., choosing toppings), use combinations.\"}]","Permutations and Combinations - GED Math - Quick Review | PDF"]