[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-523563-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-523563-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-precalculus-practice-worksheet","Permutations - Precalculus Practice Worksheet","","This document is a precalculus practice worksheet focused on the mathematical concept of permutations. It provides a structured set of exercises designed to test students' understanding of listing permutations, evaluating permutation expressions, and calculating the number of unique permutations for specific letter combinations. The content includes both basic introductory problems and more advanced critical thinking questions, accompanied by a comprehensive answer key. It is an educational resource suitable for high school or early college-level mathematics students looking to reinforce their combinatorial skills. The worksheet also features an example of simplifying algebraic expressions involving factorials and permutation notation. By engaging with these problems, students can improve their grasp of theoretical and practical permutation calculations, including cases involving repeated letters.",{"@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-precalculus-practice-worksheet/523563/",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-precalculus-practice-worksheet/523563.png","ImageObject",300,407,{"name":42,"@type":43},"acoobca","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-12","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",8,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"How do you calculate the number of unique permutations of a word?","Question",{"text":63,"@type":64},"To find the number of unique permutations of a word, divide the factorial of the total number of letters by the product of the factorials of each repeated letter's frequency.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What is the value of 7P4?",{"text":68,"@type":64},"Based on the worksheet, 7P4 equals 840 (noting that the provided text lists 1,680 for a similar expression, the standard calculation for 7P4 is 7! / (7-4)! = 840).",{"name":70,"@type":61,"acceptedAnswer":71},"Which seasons have 360 unique permutations of their letters?",{"text":72,"@type":64},"According to the critical thinking section, both 'SUMMER' and 'AUTUMN' result in 360 unique permutations when their letters are rearranged.","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},523563,1791500117,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,114,119,122,126],{"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":55,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"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":26,"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":143,"read_time":96,"preview_page_count":4},3985747870733,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Precalculus Name   \nPermutations Date  Period   \nList all possible permutations.  \n1) ☺, ☼, ♥ 2) ☺, ☼  \n3) 1, 2 4) A, B, C, taken two at a time  \nEvaluate each expression.  \n5) 􀀛 P􀀗 6) 􀀛 P􀀘  \n7) 􀀚 P􀀘 8) 􀀔􀀓 P􀀖  \n9) 􀀔􀀓 P􀀘 􀀐 􀀘 10) 􀀔􀀓 P􀀖  \nFind the number of unique permutations ofthe letters in each word.  \n11) EVERY 12) SOLO  \n13) BANDING 14) STRUTS  \n15) THERMOMETER 16) BILLIONAIRE  \nCritical thinking questions:  \n17) Name a season of the year, where if you 18) Simplify xPx 􀀐 􀀕 rearrange the letters there are 360 unique  \npermutations.  \nKuta Software-Infinite Precalculus Permutations  \nList all possible permutations.  \n1) ☺, ☼, ♥  \n☺☼♥☺♥☼  \n☼☺♥  \n☼♥☺  \n♥☺☼  \n♥☼☺  \n3) 1, 2  \n12 21  \nEvaluate each expression.  \n5) 􀀛 P􀀗  \n1,680  \n7) 􀀚 P􀀘  \n2,520  \n9) 􀀔􀀓 P􀀘 􀀐 􀀘  \n30,235  \nName  Date  Period   \n2) ☺, ☼  \n☺☼ ☼☺  \n4) A, B, C, taken two at a time  \nAB BA CA  \nAC BC CB  \n6) 􀀛 P􀀘  \n6,720  \n8) 􀀔􀀓 P􀀖 720  \n10) 􀀔􀀓 P􀀖 720  \nFind the number of unique permutations ofthe letters in each word.  \n11) EVERY 60  \n13) BANDING  \n2,520  \n15) THERMOMETER  \n831,600  \nCritical thinking questions:  \n17) Name a season of the year, where if you rearrange the letters there are 360 unique permutations.  \nSUMMER or AUTUMN  \n12) SOLO 12  \n14) STRUTS 180  \n16) BILLIONAIRE  \n3,326,400  \n18) Simplify xPx 􀀐 􀀕  \nx!􀀕  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaion9q1K4ms3s","https://ap.wps.com/l/cbCaion9q1K4ms3s","pdf",73708,"English","# Permutations Exercises\n## Listing Permutations\n## Evaluating Expressions\n## Unique Letter Permutations\n## Critical Thinking Questions","[{\"question\":\"How do you calculate the number of unique permutations of a word?\",\"answer\":\"To find the number of unique permutations of a word, divide the factorial of the total number of letters by the product of the factorials of each repeated letter's frequency.\"},{\"question\":\"What is the value of 7P4?\",\"answer\":\"Based on the worksheet, 7P4 equals 840 (noting that the provided text lists 1,680 for a similar expression, the standard calculation for 7P4 is 7! / (7-4)! = 840).\"},{\"question\":\"Which seasons have 360 unique permutations of their letters?\",\"answer\":\"According to the critical thinking section, both 'SUMMER' and 'AUTUMN' result in 360 unique permutations when their letters are rearranged.\"}]","Permutations - Precalculus Practice Worksheet | PDF",1791427021]