{"id":154308,"date":"2022-03-25T23:23:27","date_gmt":"2022-03-25T17:53:27","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/combinatorics\/"},"modified":"2022-12-31T16:23:01","modified_gmt":"2022-12-31T10:53:01","slug":"combinatorics","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/combinatorics\/","title":{"rendered":"Combinatorics"},"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\/combinatorics\/#What_is_Combinatorics\" title=\"What is Combinatorics?\">What is Combinatorics?<\/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\/combinatorics\/#What_is_Combinatorics_Combinatorial_Meaning\" title=\"What is Combinatorics? Combinatorial Meaning\">What is Combinatorics? Combinatorial Meaning<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/combinatorics\/#Combinatorics_Formula\" title=\"Combinatorics Formula\">Combinatorics Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/combinatorics\/#What_are_the_Combinatorics_Applications\" title=\"What are the Combinatorics Applications?\">What are the Combinatorics Applications?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/combinatorics\/#Some_of_the_Other_Combinatorics_Applications_are_as_Follows\" title=\"Some of the Other Combinatorics Applications are as Follows:\">Some of the Other Combinatorics Applications are as Follows:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/combinatorics\/#What_are_Permutation_and_Combination\" title=\"What are Permutation and Combination?\">What are Permutation and Combination?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/combinatorics\/#Combinatorics_Problems_-_Solved_Example\" title=\"Combinatorics Problems &#8211; Solved Example\">Combinatorics Problems &#8211; Solved Example<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Combinatorics\"><\/span>What is Combinatorics?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Combinatorics is a branch of mathematics that deals with the study of finite or countable discrete structures. In other words, it is the study of the number of possible ways that a certain number of objects can be arranged or combined.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154307 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/combinatorics.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/combinatorics.jpg?v=1648230803 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/combinatorics-300x212.jpg?v=1648230803 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Combinatorics_Combinatorial_Meaning\"><\/span>What is Combinatorics? Combinatorial Meaning<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Combinatorics is the study of counting, shapes and structures using mathematical techniques. It is often considered a branch of discrete mathematics.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Combinatorics_Formula\"><\/span>Combinatorics Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The binomial theorem states that for every positive integer n, there is a unique binomial coefficient. The binomial coefficient is the coefficient of the x raised to the power of n in the expansion of<\/p>\n<p>(x + y)n.<\/p>\n<p>The binomial theorem can be proved using induction. The basis of the induction is that the theorem is true for n = 0. The induction step is that the theorem is also true for n = k, where k is a positive integer greater than 0.<\/p>\n<p>The binomial theorem can also be derived from the fact that the binomial coefficient is the coefficient of the x raised to the power of n in the expansion of (x + y)n. To see this, note that the expansion of (x + y)n is<\/p>\n<p>Each term in this expansion can be written as a product of two factors: a term in the expansion of xn and a term in the expansion of yn. The coefficient of the x raised to the power of n in the expansion of (x + y)n is the product of the coefficient of the x raised to the power of n in the expansion of xn and the coefficient of the y raised to the power of n in the expansion of yn.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_the_Combinatorics_Applications\"><\/span>What are the Combinatorics Applications?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Combinatorics is the study of finite or countable discrete structures. It is a branch of mathematics that deals with the enumeration, combination, and permutation of objects.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Some_of_the_Other_Combinatorics_Applications_are_as_Follows\"><\/span>Some of the Other Combinatorics Applications are as Follows:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>-Finding the number of ways to partition a set<br \/>\n-Finding the number of ways to choose k objects from a set<br \/>\n-Finding the number of ways to choose m objects from a set, when order matters<br \/>\n-Finding the number of ways to choose k objects from a set, when order does not matter<br \/>\n-Finding the number of ways to partition a set into two parts<br \/>\n-Finding the number of ways to partition a set into three parts<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Permutation_and_Combination\"><\/span>What are Permutation and Combination?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Permutation is a mathematical term for the number of different ways that a given number of items can be arranged. For example, if you have three items, there are six permutations (3!), which is equal to 3x2x1 = 6. This is because there are three different ways to order the first item, two different ways to order the second item, and one way to order the third item.<\/p>\n<p>Combination is a mathematical term for the number of different ways that a given number of items can be selected from a given set of items. For example, if you have three items and you want to select two, there are six combinations (3!\/(2!x1!)), which is equal to 3&#215;2 = 6. This is because there are three different ways to select the first item, two different ways to select the second item, and one way to select the third item.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Combinatorics_Problems_-_Solved_Example\"><\/span>Combinatorics Problems &#8211; Solved Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Problem:<\/p>\n<p>In how many ways can a committee of six be chosen from a group of ten people?<\/p>\n<p>There are 10! or 3,628,800 ways to choose a committee of six people from a group of ten people.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is Combinatorics? Combinatorics is a branch of mathematics that deals with the study of finite or countable discrete structures. [&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":"Combinatorics","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Combinatorics topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online.","custom_permalink":"maths\/combinatorics\/"},"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>Combinatorics - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Combinatorics topic of Maths in details explained by subject experts on infinitylearn.com. 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