{"id":17938,"date":"2019-09-02T13:02:40","date_gmt":"2019-09-02T18:02:40","guid":{"rendered":"http:\/\/www.kaptest.com\/blog\/prep\/?p=17938"},"modified":"2020-09-11T20:40:58","modified_gmt":"2020-09-11T20:40:58","slug":"gre-quantitative-combinations-and-permutations","status":"publish","type":"post","link":"https:\/\/wpapp.kaptest.com\/study\/gre\/gre-quantitative-combinations-and-permutations\/","title":{"rendered":"GRE Quantitative: Combinations and Permutations"},"content":{"rendered":"<div class=\"row content text\">\n<div class=\"col-md-7 no-padding\">Let\u2019s do some GRE math practice.\u00a0Combinations and permutations problems\u00a0often leave students wondering where on earth to begin. Knowing the equation for each operation is helpful, but not enough\u2014you also must be able to determine which formula is necessary to answer the question at hand.<\/div>\n<div class=\"the-content\">\n&nbsp;<br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-0  el_before_av_heading  avia-builder-el-first  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Combinations and Permutations on the GRE<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nThe rule of thumb is that combinations are unordered and permutations are ordered, but what does that mean? We like illustrating the difference using a social club.<\/p>\n<ul>\n<li>Imagine the social club has\u00a010 different members\u00a0and you\u2019re asked, \u201c<i>How many groups of 3 members\u00a0can you choose from the social club to make a party committee?<\/i>\u201d Would you need to do combinations or permutations in order to formulate an answer? How do you know?<\/li>\n<li>Alternatively, imagine we alter the question slightly and ask, \u201c\u00a0<i>An officer slate consists of a President, a Vice President, and a Treasurer.\u00a0How many different officer slates\u00a0can you select \u00a0from the social club membership?<\/i>\u201d Is this the same question? Or is it different? Would you need to use combinations or permutations?<\/li>\n<\/ul>\n<p>The questions are, in fact, quite different. So how do you apply each method on the GRE?<br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-1  el_after_av_heading  el_before_av_image  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Solving Combinations Problems<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nThe first question (\u201c<i>How many groups of 3\u2026<\/i>\u201d) indicates that we are counting groups of 3 people, with no need to worry about which person\u00a0we choose first, second, or third\u2014i.e., order does not matter. For that reason, this is a combinations problem.<br \/>\nIn order to answer the question, we will use the combinations formula, where\u00a0<i>n<\/i>\u00a0= the total number of items (10) and\u00a0<i>k<\/i>\u00a0= the number of items selected (3). Note that\u00a0<i>k<\/i>\u00a0can equal\u00a0<i>n<\/i>, but can never be greater than\u00a0<i>n<\/i>\u00a0(we can choose all of the items in a group, but cannot choose more items than the total). Here\u2019s the combinations formula:<br \/>\n<div  class='avia-image-container  av-styling-    avia-builder-el-2  el_after_av_heading  el_before_av_image  avia-align-center '  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\"  ><div class='avia-image-container-inner'><div class='avia-image-overlay-wrap'><img class='wp-image-0 avia-img-lazy-loading-not-0 avia_image' src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2018\/02\/Screen-Shot-2017-06-01-at-1.08.50-PM.png\" alt='' title=''   itemprop=\"thumbnailUrl\"  \/><\/div><\/div><\/div><br \/>\nNote that an exclamation point means a factorial; factorial means multiplying the number times each integer below it down to 1. For instance, 4! = 4 * 3 * 2 * 1.<br \/>\nPlugging our values into the equation, we get the following (make sure you reduce numbers in the extended calculations to simplify the actual multiplying you have to do):<br \/>\n<div  class='avia-image-container  av-styling-    avia-builder-el-3  el_after_av_image  el_before_av_heading  avia-align-center '  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\"  ><div class='avia-image-container-inner'><div class='avia-image-overlay-wrap'><img class='wp-image-0 avia-img-lazy-loading-not-0 avia_image' src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2018\/02\/Screen-Shot-2017-05-31-at-10.49.15-AM-300x35.png\" alt='' title=''   itemprop=\"thumbnailUrl\"  \/><\/div><\/div><\/div><br \/>\nTherefore, we could choose 120 different groups of 3 party committees.<br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-4  el_after_av_image  el_before_av_image  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Solving Permutation Problems<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nThe second question asks, \u201c<i>How many different ways can you select a 3-person slate of officers?<\/i>\u201d This wording tells us that we should track each selection independently, rather than by groups of 3. For example, selecting Nick as President, then Kim as Vice President, then Priyanka as Treasurer\u00a0would not be the same as selecting Kim as President, then Priyanka as Vice President, then Nick as treasurer, which would not be the same as selecting Kim as President, then Nick as Vice President, then Priyanka as Treasurer, and so on\u2014i.e., order matters. For that reason, this is a permutations problem. In order to answer this question, we will use the following permutations formula:<br \/>\n<div  class='avia-image-container  av-styling-    avia-builder-el-5  el_after_av_heading  el_before_av_image  avia-align-center '  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\"  ><div class='avia-image-container-inner'><div class='avia-image-overlay-wrap'><img class='wp-image-0 avia-img-lazy-loading-not-0 avia_image' src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2018\/02\/Screen-Shot-2017-05-31-at-10.49.25-AM.png\" alt='' title=''   itemprop=\"thumbnailUrl\"  \/><\/div><\/div><\/div><br \/>\nAs you can see, the denominator is the point of difference between the combinations and permutations formulas. For any values of\u00a0<i>n<\/i>\u00a0and\u00a0<i>k<\/i>, the number of combinations we can form will always be smaller than the number of permutations we can form. This problem is no exception. Plugging our values into the equation, then reducing as much as possible, we get:<br \/>\n<div  class='avia-image-container  av-styling-    avia-builder-el-6  el_after_av_image  el_before_av_heading  avia-align-center '  itemprop=\"image\" itemscope=\"itemscope\" itemtype=\"https:\/\/schema.org\/ImageObject\"  ><div class='avia-image-container-inner'><div class='avia-image-overlay-wrap'><img class='wp-image-0 avia-img-lazy-loading-not-0 avia_image' src=\"http:\/\/www.kaptest.com\/blog\/prep\/wp-content\/uploads\/sites\/21\/2018\/02\/Screen-Shot-2017-05-31-at-10.49.31-AM-300x35.png\" alt='' title=''   itemprop=\"thumbnailUrl\"  \/><\/div><\/div><\/div><br \/>\nSo, when order matters and we track each selection differently, there are 720 different ways we can choose 3 officers.<br \/>\n<div  style='padding-bottom:10px; ' class='av-special-heading av-special-heading-h3    avia-builder-el-7  el_after_av_image  el_before_av_sidebar  '><h3 class='av-special-heading-tag '  itemprop=\"headline\"  >Pay Attention to Language<\/h3><div class='special-heading-border'><div class='special-heading-inner-border' ><\/div><\/div><\/div><br \/>\nThe\u00a0<a href=\"http:\/\/www.ets.org\/gre\" target=\"_blank\" rel=\"noopener noreferrer\">GRE test-makers<\/a>\u00a0create challenging problems by using subtle language to indicate whether you should use a combination or permutation formula to answer the question at hand. Combination questions will indicate that you need to form groups or sets; permutation questions will have words or phrases that indicate order, such as \u201cfirst, second, third\u201d or \u201chow many different ways.\u201d Some\u00a0really tricky problems can\u00a0offer up a mixture of the two.<br \/>\nAs the old adage says, \u201cpractice makes perfect\u201d\u2014the more of these problems you do (and the more corresponding explanations you read), the better prepared you will be to ace combinations and permutations questions on\u00a0<a href=\"https:\/\/www.kaptest.com\/study\/gre\/what-to-expect-on-gre-test-day\/\" target=\"_blank\" rel=\"noopener noreferrer\">GRE Test Day<\/a>.<\/p>\n<p class=\"p1\"><div  class='avia-builder-widget-area clearfix  avia-builder-el-8  el_after_av_heading  avia-builder-el-last '><div id=\"text-70\" class=\"widget clearfix widget_text\">\t\t\t<div class=\"textwidget\"><p><span data-sumome-listbuilder-embed-id=\"a78fe19e226d385662749ccaadcdccd7ecdcab651c77e3b874bfcb76a80605a7\"><\/span><\/p>\n<\/div>\n\t\t<\/div><div id=\"text-71\" class=\"widget clearfix widget_text\">\t\t\t<div class=\"textwidget\"><p><span data-sumome-listbuilder-embed-id=\"185e834399a9fdd414ded52f3f51a4735f464b8c612f006f44ffba835a649b4f\"><\/span><\/p>\n<\/div>\n\t\t<\/div><\/div><\/p>\n<\/div>\n<\/div>\n<div class=\"row center-text\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Let\u2019s do some GRE math practice.\u00a0Combinations and permutations problems\u00a0often leave students wondering where on earth to begin. Knowing the equation for each operation is helpful, but not enough\u2014you also must be able to determine which formula is necessary to answer the question at hand. &nbsp; The rule of thumb is that combinations are unordered and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27063,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[68],"tags":[69,316],"_links":{"self":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/17938"}],"collection":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/comments?post=17938"}],"version-history":[{"count":1,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/17938\/revisions"}],"predecessor-version":[{"id":34489,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/posts\/17938\/revisions\/34489"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media\/27063"}],"wp:attachment":[{"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/media?parent=17938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/categories?post=17938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpapp.kaptest.com\/study\/wp-json\/wp\/v2\/tags?post=17938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}