{"id":156272,"date":"2022-03-26T01:34:21","date_gmt":"2022-03-25T20:04:21","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/factorial-simplifying-factorial-expressions-and-solved-examples\/"},"modified":"2022-12-22T21:37:52","modified_gmt":"2022-12-22T16:07:52","slug":"factorial-simplifying-factorial-expressions-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/","title":{"rendered":"Factorial &#8211; Simplifying Factorial Expressions and Solved Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#Explain_in_Detail_Simplifying_Factorial_Expressions\" title=\"Explain in Detail :Simplifying Factorial Expressions\">Explain in Detail :Simplifying Factorial Expressions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#Simplifying_Negative_Integer_Expressions\" title=\"Simplifying Negative Integer Expressions\">Simplifying Negative Integer Expressions<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#Simplifying_Negative_Integer\" title=\"Simplifying Negative Integer\">Simplifying Negative Integer<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#Solved_Example\" title=\"Solved Example\">Solved Example<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Explain_in_Detail_Simplifying_Factorial_Expressions\"><\/span>Explain in Detail :Simplifying Factorial Expressions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A factorial expression is an algebraic expression that is composed of the product of all positive integers from 1 to a given number. Factorial expressions can be simplified by cancelling out common factors. For example, the factorial expression 5! can be simplified to 5*4*3*2*1.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156271 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/factorial-simplifying-factorial-expressions-and-solved-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/factorial-simplifying-factorial-expressions-and-solved-examples.jpg?v=1648238658 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/factorial-simplifying-factorial-expressions-and-solved-examples-300x212.jpg?v=1648238658 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Simplifying_Negative_Integer_Expressions\"><\/span>Simplifying Negative Integer Expressions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To simplify a negative integer expression, divide the expression by -1.<\/p>\n<p dir=\"ltr\">Problem solving is perhaps the best way to see mathematics in action. So here we are to take you through the problems that will significantly help you learn how to simplify factorial expressions.<\/p>\n<p dir=\"ltr\">In order to simplify factorial expressions using variables that&#8217;re there in the numerator and denominator\u2014 we would require to produce common factors in both locations such that they can be canceled. Because, this is of course our objective.<\/p>\n<p dir=\"ltr\">The key is to establish a comparison between the factorials as well identify which amongst them is higher in value. Let\u2019s say we seek to compare the factorials ({n + 4}!(n+4)! And {n + 2}!(n+ 2)!<\/p>\n<p dir=\"ltr\">It is pretty obvious to observe that {n + 4}! &gt; {n + 2}! Is true for all values of \u2018n\u2019 inasmuch as the factorial is interpreted, that is to say, the items in the interior of the parenthesis is a whole number \u2265 zero (0).<\/p>\n<p dir=\"ltr\">Thus, this suggests that we can stretch {n + 4}! Until the expression {n+2}! Takes shape into the sequence.<\/p>\n<p dir=\"ltr\">Like this below:-<\/p>\n<p dir=\"ltr\">(N+4)! = (N+3). (N+3) (N+2)!<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Simplifying_Negative_Integer\"><\/span>Simplifying Negative Integer<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Let\u2019s take for example {n &#8211; 5}! And {n &#8211; 2}! In such a situation, we are subtracting the variable by some number. Keep in mind that here the bigger expression is the one with smaller subtrahend, or the value that\u2019s subtracted from the minuend. Hence, this suggests that {n &#8211; 2}! &gt; {n &#8211; 5}!<\/p>\n<p dir=\"ltr\">This further concludes that the expression {n &#8211; 2}! Will have {n &#8211; 5}! In its expanded form<\/p>\n<p dir=\"ltr\">(N -2)! = (N-2). (N-3) . (N-4) . (N-5)!<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Solved_Example\"><\/span>Solved Example<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Problem 1<\/p>\n<p dir=\"ltr\">How many different ways can 7 students in a relay race come 1st, 2nd and 3rd?<\/p>\n<p dir=\"ltr\">Solution 1<\/p>\n<p dir=\"ltr\">Seeing that it is a long-drawn list, thus, if 7 students are named T, U, V, W, X, Y, Z<\/p>\n<p dir=\"ltr\">Then the list involves:<\/p>\n<p dir=\"ltr\">TUV, TUW, TUX, TUY, TUZ, TVU, TVW, TVX, TVY&#8230; etc<\/p>\n<p dir=\"ltr\">Using the formula \u2013 7! (7\u22123)! = 7! 4!<\/p>\n<p dir=\"ltr\">Next, we will write the multiplications out in full:<\/p>\n<p dir=\"ltr\">7* 6 * 5 * 4 * 3 * 14 * 3 * 2 * 1   = 7 * 6 * 5<\/p>\n<p dir=\"ltr\">That was neat. The multiplication of {4 \u00d7 3 \u00d7 2 \u00d7 } &#8220;invalidated&#8221;, giving up only 7 \u00d7 6 \u00d7 5. And:<\/p>\n<p dir=\"ltr\">7 * 6 * 5 = 210<\/p>\n<p dir=\"ltr\">Thus, as an answer, we get 210 different ways by which 7 students secure positions at 1st, 2nd and 3rd.<\/p>\n<p dir=\"ltr\">And you\u2019re done!<\/p>\n<p dir=\"ltr\">Problem 2<\/p>\n<p dir=\"ltr\">How many ways can we arrange 4 alphabets from the start (without repeating)?<\/p>\n<p dir=\"ltr\">Solution 2<\/p>\n<p dir=\"ltr\">In order to determine the equals, you need to simply multiply the positive integers altogether that are less than or equal to (\u2264) 4. Now, likewise<\/p>\n<p dir=\"ltr\">For 1 Alphabet &#8220;a&#8221; there is solely 1 way: 1\u00d71 = (a)<\/p>\n<p dir=\"ltr\">For 2 alphabet &#8220;ab&#8221; there are 2 ways: 1\u00d72= (ab, ba)<\/p>\n<p dir=\"ltr\">For 3 Alphabet &#8220;abc&#8221; there are 6 ways: 1\u00d72\u00d73 = (abc, acb, bac, bca, cab, cba)<\/p>\n<p dir=\"ltr\">For 4 Alphabets &#8220;abcd&#8221; there are 24 ways: 1\u00d72\u00d73\u00d74= (abcd, acbd, adbc, adcb, abdc, acdb, bacd, bcad, bcda, bdac, bdca, badc, cabd, cbad, cbda, cdab,cdba, cadb, dabc, dacb, dbac, dbca, dcab, dcba)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Explain in Detail :Simplifying Factorial Expressions A factorial expression is an algebraic expression that is composed of the product of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Factorial - Simplifying Factorial Expressions and Solved Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Factorial topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","custom_permalink":"maths\/factorial\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Factorial - Simplifying Factorial Expressions and Solved Examples - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Factorial topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Factorial - Simplifying Factorial Expressions and Solved Examples - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"Learn about Factorial topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-25T20:04:21+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-12-22T16:07:52+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/factorial-simplifying-factorial-expressions-and-solved-examples.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"vipin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Factorial - Simplifying Factorial Expressions and Solved Examples - Infinity Learn by Sri Chaitanya","description":"Learn about Factorial topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/","og_locale":"en_US","og_type":"article","og_title":"Factorial - Simplifying Factorial Expressions and Solved Examples - Infinity Learn by Sri Chaitanya","og_description":"Learn about Factorial topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","og_url":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2022-03-25T20:04:21+00:00","article_modified_time":"2022-12-22T16:07:52+00:00","og_image":[{"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/factorial-simplifying-factorial-expressions-and-solved-examples.jpg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"vipin","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#primaryimage","inLanguage":"en-US","url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/factorial-simplifying-factorial-expressions-and-solved-examples.jpg?v=1648238658","contentUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/factorial-simplifying-factorial-expressions-and-solved-examples.jpg?v=1648238658","width":606,"height":428},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/","name":"Factorial - Simplifying Factorial Expressions and Solved Examples - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"primaryImageOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#primaryimage"},"datePublished":"2022-03-25T20:04:21+00:00","dateModified":"2022-12-22T16:07:52+00:00","description":"Learn about Factorial topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/maths\/factorial\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Factorial &#8211; Simplifying Factorial Expressions and Solved Examples"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2"},"headline":"Factorial &#8211; Simplifying Factorial Expressions and Solved Examples","datePublished":"2022-03-25T20:04:21+00:00","dateModified":"2022-12-22T16:07:52+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#webpage"},"wordCount":512,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/factorial\/#primaryimage"},"thumbnailUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/factorial-simplifying-factorial-expressions-and-solved-examples.jpg","articleSection":["Maths"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2","name":"vipin","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","caption":"vipin"},"sameAs":["http:\/\/surge.infinitylearn.com"],"url":"https:\/\/infinitylearn.com\/surge\/author\/vipin\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/156272"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=156272"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/156272\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=156272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=156272"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=156272"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=156272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}