{"id":153648,"date":"2022-03-25T22:39:26","date_gmt":"2022-03-25T17:09:26","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/combination\/"},"modified":"2024-08-29T14:45:09","modified_gmt":"2024-08-29T09:15:09","slug":"combination","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/combination\/","title":{"rendered":"Combination"},"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\/combination\/#What_are_Combinations\" title=\"What are Combinations? \">What are Combinations? <\/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\/combination\/#Formula_of_Combinations\" title=\"Formula of Combinations \">Formula of Combinations <\/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\/combination\/#Relationship_Between_Permutation_and_Combination\" title=\"Relationship Between Permutation and Combination\">Relationship Between Permutation and Combination<\/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\/combination\/#Practical_Applications_of_Combinations\" title=\"Practical Applications of Combinations \">Practical Applications of Combinations <\/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\/combination\/#Theorems_on_Combinations\" title=\"Theorems on Combinations \">Theorems on Combinations <\/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\/combination\/#Examples_of_Combinations\" title=\"Examples of Combinations\">Examples of Combinations<\/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\/combination\/#Practice_Questions_on_Combinations\" title=\"Practice Questions on Combinations \">Practice Questions on Combinations <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/combination\/#Combinations_FAQs\" title=\"Combinations: FAQs \">Combinations: FAQs <\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/combination\/#Does_Order_Matter_in_Combinations\" title=\"Does Order Matter in Combinations?\">Does Order Matter in Combinations?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/combination\/#What_Are_Combinations_In_Numbers\" title=\"What Are Combinations In Numbers?\">What Are Combinations In Numbers?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/combination\/#What_is_the_Formula_to_calculate_the_number_of_Combinations_possible\" title=\"What is the Formula to calculate the number of Combinations possible?\">What is the Formula to calculate the number of Combinations possible?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span style=\"font-weight: 400;\">In mathematics, a combination refers to the selection of items from a larger set. In the case of combinations, the order of selection is irrelevant. This concept is fundamental in many areas of mathematics, especially in probability and statistics. Unlike permutations, where order matters, combinations are all about choosing a specific number of items without worrying about their arrangement. <\/span><span style=\"font-weight: 400;\">This article will discuss combinations, their definitions, formulas, and examples. <\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-a-circle\/\">Area of a Circle<\/a><\/strong><\/p>\n<h2><span style=\"font-weight: 400;\">What are Combinations? <\/span><\/h2>\n<p><span style=\"font-weight: 400;\">A combination is defined as a selection of items from a larger set, where the sequence in which the items are selected does not matter. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example, consider a simple set consisting of three elements: P, Q, and R. If we are to select two items from this set, the possible combinations would be PQ, PR, and QR. Notice that PQ is considered the same as QP in combinations because the order of selection is not important.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Formula of Combinations <\/span><\/h2>\n<p><span style=\"font-weight: 400;\">The combinations formula is a mathematical tool used to determine the number of possible groups or subsets that can be formed by selecting a certain number of objects (r) from a larger set of distinct objects (n), without regard to the order in which the objects are chosen.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The formula for combinations is given by: <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Combination Formula = <\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">n!<\/span><span style=\"font-weight: 400;\">r! (n &#8211; r)!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Where: n! (n factorial) is the product of all positive integers up to n.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">r! (r factorial) is the product of all positive integers up to r.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(n\u2212r)! is the factorial of the difference between n and r.<\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check:<a href=\"https:\/\/infinitylearn.com\/surge\/maths\/faces-edges-and-vertices\/\"> Vertices, Faces and Edges<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Relationship_Between_Permutation_and_Combination\"><\/span><span style=\"font-weight: 400;\">Relationship Between Permutation and Combination<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">A combination is a specific type of permutation where the order of selection is not important. In permutations, different orders of selection are counted as distinct arrangements, whereas, in combinations, they are treated as the same. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example, in combination AB and BA are the same while in permutation these both are considered different. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">As a result, the number of permutations of a set is always greater than or equal to the number of combinations.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The relationship between permutations and combinations is captured by the formula:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\">r<\/span> <span style=\"font-weight: 400;\">r!<\/span><span style=\"font-weight: 400;\"> <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Where, <\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> is the number of permutations and <\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> is the number of combinations. <\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Practical Applications of Combinations <\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Combinations have vast applications in various fields, including statistics, probability, and everyday decision-making processes. Combinations help in calculating the odds in a card game, determining possible outcomes in a survey, or selecting a team from a group of players. Combinations help in analysing possibilities in a systematic way. <\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/area-of-a-circle\/\">Area of a Circle<\/a><\/strong><\/p>\n<h2><span style=\"font-weight: 400;\">Theorems on Combinations <\/span><\/h2>\n<p><b>Theorem: Prove that <\/b> <b>n<\/b><b>P<\/b><b>r <\/b><b> = r!<\/b><b>n<\/b><b>C<\/b><b>r<\/b><\/p>\n<p><b>Proof:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">By the definition of Permutations: <\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">n!<\/span><span style=\"font-weight: 400;\">(n &#8211; r)!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Similarly, by the definition of Combinations: <\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">n!<\/span><span style=\"font-weight: 400;\">r! (n &#8211; r)!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, the Relation Between Permutations and Combinations:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">n!<\/span><span style=\"font-weight: 400;\">r! (n &#8211; r)!<\/span><span style=\"font-weight: 400;\"> <\/span><\/p>\n<p><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">P<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\">r! <\/span><span style=\"font-weight: 400;\"> <\/span><\/p>\n<p><b>n<\/b><b>P<\/b><b>r <\/b><b> = r!<\/b><b>n<\/b><b>C<\/b><b>r<\/b><\/p>\n<p><span style=\"font-weight: 400;\">This confirms that the theorem holds true.<\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube\/\">CUBE<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Examples_of_Combinations\"><\/span><span style=\"font-weight: 400;\">Examples of Combinations<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><b>Example 1:<\/b><span style=\"font-weight: 400;\"> Suppose you have a set of four items: Apple, Banana, Cherry, and Durian, and you want to choose any three items from this set to make a milkshake. Find the number of possible combinations. <\/span><\/p>\n<p><b>Ans. <\/b><span style=\"font-weight: 400;\">According to the combination formula, the number of possible combinations is:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">n!<\/span><span style=\"font-weight: 400;\">r! (n &#8211; r)!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Here, <\/span> <span style=\"font-weight: 400;\">n = 4<\/span><\/p>\n<p><span style=\"font-weight: 400;\">r = 3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, <\/span><span style=\"font-weight: 400;\">4<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">4!<\/span><span style=\"font-weight: 400;\">3! (4 &#8211; 3)!<\/span><span style=\"font-weight: 400;\"> =<\/span><span style=\"font-weight: 400;\">4!<\/span><span style=\"font-weight: 400;\">3! (1)!<\/span><span style=\"font-weight: 400;\"> =  4<\/span><span style=\"font-weight: 400;\"> <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, the possible combinations are four in number. The possible combinations would be ABC, ABD, ACD, and BCD. Where A is apple, B is banana, C is cherry, and D is durian. <\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/average\/\">Average<\/a><\/strong><\/p>\n<p><b>Example 2: <\/b><span style=\"font-weight: 400;\">Consider a set of 10 elements, and you want to select 3 elements from this set. Find the number of possible combinations for this situation. <\/span><\/p>\n<p><b>Ans. <\/b><span style=\"font-weight: 400;\">The number of possible subsets can be calculated using the combination formula:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">n!<\/span><span style=\"font-weight: 400;\">r! (n &#8211; r)!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Here, n = 10 and r = 3 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">10<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">10!<\/span><span style=\"font-weight: 400;\">3! (10 &#8211; 3)!<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">10!<\/span><span style=\"font-weight: 400;\">3! (7)!<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">10 <\/span><span style=\"font-weight: 400;\"> 9 <\/span><span style=\"font-weight: 400;\"> 8 <\/span><span style=\"font-weight: 400;\"> 7!<\/span><span style=\"font-weight: 400;\">3 <\/span><span style=\"font-weight: 400;\"> 2 <\/span><span style=\"font-weight: 400;\"> 1 (7)!<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">10 <\/span><span style=\"font-weight: 400;\"> 9 <\/span><span style=\"font-weight: 400;\"> 8<\/span><span style=\"font-weight: 400;\">3 <\/span><span style=\"font-weight: 400;\"> 2<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">720<\/span><span style=\"font-weight: 400;\">6<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">360<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> = 120<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Thus, there are 120 different ways to select 3 items from a set of 10.<\/span><\/p>\n<p><b>Example 3: <\/b><span style=\"font-weight: 400;\">Consider a set of 5 fruits, and you want to select 3 fruits from this set. Find the number of possible combinations for this situation. <\/span><\/p>\n<p><b>Ans. <\/b><span style=\"font-weight: 400;\">The number of possible subsets can be calculated using the combination formula:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">r<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">n!<\/span><span style=\"font-weight: 400;\">r! (n &#8211; r)!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Here, n = 5 and r = 3 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">5<\/span><span style=\"font-weight: 400;\">C<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">5!<\/span><span style=\"font-weight: 400;\">3! (5 &#8211; 3)!<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">5!<\/span><span style=\"font-weight: 400;\">3! (2)!<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">5 <\/span><span style=\"font-weight: 400;\"> 4<\/span><span style=\"font-weight: 400;\"> 2 <\/span><span style=\"font-weight: 400;\"> 1<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">20 <\/span><span style=\"font-weight: 400;\"> 2<\/span><span style=\"font-weight: 400;\"> = 10<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Thus, there are 10 different ways to select 3 items from a set of 5.<\/span><\/p>\n<p style=\"text-align: center;\"><strong>Also Check:<a href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/\"> Circumstance of Circle<\/a><\/strong><\/p>\n<h2><span style=\"font-weight: 400;\">Practice Questions on Combinations <\/span><\/h2>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A group of 4 basketball players, A, B, C, and D, needs to form a team of 2 players. In how many ways can the team be selected?<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A committee of 3 people is to be formed from a group of 5 members, P, Q, R, S, and T. How many different committees can be formed?<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">There are 6 friends, M, N, O, P, Q, and R. How many ways can a team of 3 people be selected from this group?<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A class has 7 students, X, Y, Z, W, V, U, and T. If the teacher needs to pick a group of 4 students to represent the class in a quiz, how many different groups can be formed?<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">In a chess club of 5 members, E, F, G, H, and I, a sub-team of 3 members is to be selected for a tournament. How many possible selections are there?<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A team of 2 swimmers is to be formed from a group of 5 swimmers, K, L, M, N, and O. How many ways can this be done?<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">From a set of 6 cards labelled A, B, C, D, E, and F, how many ways can a pair of 2 cards be selected?<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A group of 4 dancers, P, Q, R, and S, need to select 3 dancers for a performance. In how many ways can the selection be made?<\/span><\/li>\n<\/ol>\n<h2><span style=\"font-weight: 400;\">Combinations: FAQs <\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Does_Order_Matter_in_Combinations\"><\/span>Does Order Matter in Combinations?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tNo, the order does not matter in combinations. The focus is on the selection of items, not on the arrangement.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_Are_Combinations_In_Numbers\"><\/span>What Are Combinations In Numbers?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tCombinations are selections where the order of the selected objects does not matter. When selecting r objects out of a given set of n objects, the number of combinations is determined using factorials. The formula for combinations is given by: Combination Formula = nCr = n! \/ (r! * (n - r)!) This formula calculates the number of different subgroups (combinations) that can be formed from the given larger group of objects.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_Formula_to_calculate_the_number_of_Combinations_possible\"><\/span>What is the Formula to calculate the number of Combinations possible?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe formula to calculate the number of possible combinations is given below: Combination Formula = nCr = n! \/ (r! * (n - r)!)\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Does Order Matter in Combinations?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"No, the order does not matter in combinations. The focus is on the selection of items, not on the arrangement.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What Are Combinations In Numbers?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Combinations are selections where the order of the selected objects does not matter. When selecting r objects out of a given set of n objects, the number of combinations is determined using factorials. The formula for combinations is given by: Combination Formula = nCr = n! \/ (r! * (n - r)!) This formula calculates the number of different subgroups (combinations) that can be formed from the given larger group of objects.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the Formula to calculate the number of Combinations possible?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The formula to calculate the number of possible combinations is given below: Combination Formula = nCr = n! \/ (r! * (n - r)!)\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>In mathematics, a combination refers to the selection of items from a larger set. In the case of combinations, the [&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":"Combination","_yoast_wpseo_title":"Combination - Definition, Formula, Theorems, Relationship & Application","_yoast_wpseo_metadesc":"Combination refers to a selection of items from a larger set without regard to the order of the items. Choose a subset of objects from collection.","custom_permalink":"maths\/combination\/"},"categories":[13],"tags":[8079],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Combination - Definition, Formula, Theorems, Relationship &amp; Application<\/title>\n<meta name=\"description\" content=\"Combination refers to a selection of items from a larger set without regard to the order of the items. 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