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Solutions section begins by applying permutation and combination formulas and multiplying choices to obtain final counts.",{"@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-arrangements-and-passwords-practice-worksheet/274707/",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-arrangements-and-passwords-practice-worksheet/274707.png","ImageObject",300,407,{"name":42,"@type":43},"Alex Sinclair","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-20","2026-09-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you count 3-digit codes when repeats are allowed from digits {1,2,3,4,5}?","Question",{"text":63,"@type":64},"Each of the three positions has 5 choices. Multiply: 5 × 5 × 5 = 5^3 possible codes.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you count 4-digit even numbers from digits {0,1,2,3}?",{"text":68,"@type":64},"The first digit cannot be 0. The last digit must be 0 or 2. Count remaining choices consistently for each case of the first and last digits and sum them to get the total.",{"name":70,"@type":61,"acceptedAnswer":71},"What is the difference in counting when order matters for 2-letter words from DAVE?",{"text":72,"@type":64},"When order matters, DA and AD are different. First count choices for the first letter and second letter without replacement, then multiply to get the number of ordered outcomes.","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},274707,1789481917,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"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":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":111,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":118},1099523882182,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","| WORKSHEET :\u003Cbr>\u003Cbr>Permutations |\n| --- |\n| 1) How many unique 3 digit codes can be created from the 5 digits {1, 2, 3, 4, 5} if repeats are possible?\u003Cbr>2) In how many ways can I create 2 letter words from the letters in the word DAVE? Any 2 letters form a 2 letter word.\u003Cbr>3) Malcolm has to choose 5 numbers for his password (from digits 0 to 9) and repeat digits are not possible. How many different arrangements of numbers could Malcolm choose?\u003Cbr>4) 10 students have appeared for a test in which the top three will get a prize. How many possible ways are there to get the prize winners?\u003Cbr>5) How many unique passwords can be made from 4 letters if repeat letters are possible?\u003Cbr>6) How many permutations of 3 vowels can be made from the vowels (a,e,i,o,u) without any repeat letters?\u003Cbr>7) How many unique passwords can be made from 2 letters and 3 digits (0 to 9) if repeats are possible?\u003Cbr>8) How many 4-digit even numbers can be created from the digits {0, 1, 2, 3}?\u003Cbr>9) There are 6 people who will sit in a row but out of them, Ronnie, will always be left of Annie and Rachel will always be right of Annie. How many row arrangements are possible?\u003Cbr>10) In how many ways can the name Saige be re-arranged such that the letter \"i\" comes to the right of the letter \"g\"? |\n\nName: Date:  \n\n| WORKSHEET:\u003Cbr>\u003Cbr>Combinations |\n| --- |\n| 1) In how many ways can Max select 3 toppings from 10 available toppings for his pizza?\u003Cbr>2) In how many ways can coach Johnson select 5 young women for the basketball team if 15 players try out?\u003Cbr>3) How many different committees of 5 people can be chosen from 10 people?\u003Cbr>4) Jones is the Chairman of a committee. In how many ways can a committee of 5 be chosen from 10 people given that Jones must be one of them?\u003Cbr>5) You just bought 3 tickets to the Yankees and you have 5 friends you could invite. How many different combinations of friends could you choose to join you at the game?\u003Cbr>6) Any two lines in a plane form at most one intersection. If there are 10 distinct lines, then what is the maximum number of intersections possible?\u003Cbr>7) From previous lessons we learned a line can be formed from any two points. If there are 5 points in a plane then what is the maximum number of unique lines that can be drawn between the points?\u003Cbr>8) Six friends want to play enough games of chess to be sure every one plays everyone else. How many games will they have to play?\u003Cbr>9) 16 teams enter a soccer competition. They are divided up into four Pools (A, B, C and D) of four teams each.\u003Cbr>Every team plays one match against the other teams in its Pool.\u003Cbr>After the Pool matches are completed:\u003Cbr>• the winner of Pool A plays the second placed team of Pool B\u003Cbr>• the winner of Pool B plays the second placed team of Pool A\u003Cbr>• the winner of Pool C plays the second placed team of Pool D\u003Cbr>• the winner of Pool D plays the second placed team of Pool C\u003Cbr>The winners of these four matches then play semi-finals, and the winners of the semi-finals play in the final.\u003Cbr>How many matches are played altogether?\u003Cbr>10) A lottery ticket requires players to select 5 distinct numbers from 00 to 99 to appear on the ticket. How many unique tickets are possible? |\n\n\n| ANSWERS :\u003Cbr>\u003Cbr>Permutations |\n| --- |\n| 1) How many unique 3 digit codes can be created from the 5 digits {1, 2, 3, 4, 5} if repeats are possible?\u003Cbr>5 choices × 5 choices × 5 choices = 53 possible 3 digit codes including repeats\u003Cbr>2) In how many ways can I create 2 letter words from the letters in the word DAVE? Any 2 letters form a 2 letter word.\u003Cbr>Choose two letters from four = P(4,2) = 4!/2! = 4 choices × 3 choices = 12. Order matters i.e. DA is a different word than AD.\u003Cbr>3) Malcolm has to choose 5 numbers for his password (from digits 0 to 9) and repeat digits are not possible. How many different arrangements of numbers could Malcolm choose?\u003Cbr>P(10,5) = 10!/5! = 10 × 9 × 8 × 7 × 6\u003Cbr>4) 10 students have appeared for a test in which the top three will get un","cbCaiojPwhQ4Jynp","https://ap.wps.com/l/cbCaiojPwhQ4Jynp","pdf",176435,"English","# Permutations\n## Unique codes and passwords (repeats allowed)\n## Words and ordered selections\n## Arrangements with no repeats\n## Even numbers and positional constraints\n## Seating and name re-arrangement\n# Combinations\n## Selecting toppings and team members\n## Committees with required members\n## Friend invitations and lottery tickets\n## Maximum intersections and lines from points\n## Chess scheduling and tournament matches","[{\"question\":\"How do you count 3-digit codes when repeats are allowed from digits {1,2,3,4,5}?\",\"answer\":\"Each of the three positions has 5 choices. Multiply: 5 × 5 × 5 = 5^3 possible codes.\"},{\"question\":\"How do you count 4-digit even numbers from digits {0,1,2,3}?\",\"answer\":\"The first digit cannot be 0. The last digit must be 0 or 2. Count remaining choices consistently for each case of the first and last digits and sum them to get the total.\"},{\"question\":\"What is the difference in counting when order matters for 2-letter words from DAVE?\",\"answer\":\"When order matters, DA and AD are different. First count choices for the first letter and second letter without replacement, then multiply to get the number of ordered outcomes.\"}]","Permutations - Arrangements and Passwords Practice Worksheet | PDF"]