{"id":4759,"date":"2025-06-09T02:22:01","date_gmt":"2025-06-09T02:22:01","guid":{"rendered":"https:\/\/thecompanyboy.com\/?p=4759"},"modified":"2025-06-09T02:22:01","modified_gmt":"2025-06-09T02:22:01","slug":"gmat-combinatorics-statistics","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/drive\/gmat-combinatorics-statistics\/","title":{"rendered":"GMAT Statistics Combinatorics"},"content":{"rendered":"<div id=\"pl-4759\" class=\"panel-layout\">\n<div id=\"pg-4759-0\" class=\"panel-grid panel-no-style\">\n<div id=\"pgc-4759-0-0\" class=\"panel-grid-cell\" data-weight=\"1\">\n<div id=\"panel-4759-0-0-0\" class=\"so-panel widget widget_black-studio-tinymce widget_black_studio_tinymce panel-first-child panel-last-child\" data-index=\"0\" data-style=\"{&quot;background_image_attachment&quot;:false,&quot;background_display&quot;:&quot;tile&quot;}\">\n<div class=\"textwidget\">\n<p><strong>Author<\/strong>: Brian Galvin<\/p>\n<p><strong>Size of File: <\/strong>13MB<\/p>\n<p><strong>Number Of Pages: <\/strong>297<\/p>\n<p><strong>Language: <\/strong>English<\/p>\n<p><strong>Category :<\/strong> GMAT<\/p>\n<p><strong>Page Quality: <\/strong>Good<\/p>\n<p><a href=\"https:\/\/drive.google.com\/open?id=1z5CD1TCCkYkRI4-5KvYB_oTsQLrrAvva\" target=\"_blank\" rel=\"noopener\">GMAT Statistics Combinatorics Notes Download Link<\/a><\/p>\n<p data-start=\"0\" data-end=\"113\">Here\u2019s a structured guide on <strong data-start=\"29\" data-end=\"64\">GMAT Statistics &amp; Combinatorics<\/strong> to help you master these concepts efficiently.<\/p>\n<h3 data-start=\"120\" data-end=\"174\"><strong data-start=\"122\" data-end=\"172\">GMAT Statistics &amp; Combinatorics Strategy Guide<\/strong><\/h3>\n<h2 data-start=\"176\" data-end=\"216\"><strong data-start=\"179\" data-end=\"214\">1. Statistics Concepts for GMAT<\/strong><\/h2>\n<h3 data-start=\"218\" data-end=\"240\"><strong data-start=\"222\" data-end=\"240\">Mean (Average)<\/strong><\/h3>\n<ul data-start=\"241\" data-end=\"445\">\n<li data-start=\"241\" data-end=\"330\">Formula: <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Mean=\u2211valuesnumber\u00a0of\u00a0values\\text{Mean} = \\frac{\\sum \\text{values}}{\\text{number of values}}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord text\"><span class=\"mord\">Mean<\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord text\">number\u00a0of\u00a0values<\/span><span class=\"mop op-symbol small-op\">\u2211<\/span><span class=\"mord text\">values<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"331\" data-end=\"445\">Properties:\n<ul data-start=\"349\" data-end=\"445\">\n<li data-start=\"349\" data-end=\"385\">The mean is sensitive to outliers.<\/li>\n<li data-start=\"388\" data-end=\"445\">The sum of deviations from the mean is always <strong data-start=\"436\" data-end=\"444\">zero<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3 data-start=\"447\" data-end=\"463\"><strong data-start=\"451\" data-end=\"461\">Median<\/strong><\/h3>\n<ul data-start=\"464\" data-end=\"732\">\n<li data-start=\"464\" data-end=\"530\">The middle value when numbers are arranged in ascending order.<\/li>\n<li data-start=\"531\" data-end=\"595\">If there are <strong data-start=\"546\" data-end=\"553\">odd<\/strong> numbers, the median is the middle term.<\/li>\n<li data-start=\"596\" data-end=\"683\">If there are <strong data-start=\"611\" data-end=\"619\">even<\/strong> numbers, the median is the average of the two middle numbers.<\/li>\n<li data-start=\"684\" data-end=\"732\"><strong data-start=\"686\" data-end=\"730\">Less affected by outliers than the mean.<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"734\" data-end=\"748\"><strong data-start=\"738\" data-end=\"746\">Mode<\/strong><\/h3>\n<ul data-start=\"749\" data-end=\"924\">\n<li data-start=\"749\" data-end=\"799\">The most frequently occurring number in a set.<\/li>\n<li data-start=\"800\" data-end=\"924\">A set may have <strong data-start=\"817\" data-end=\"840\">one mode (unimodal)<\/strong>, <strong data-start=\"842\" data-end=\"873\">multiple modes (multimodal)<\/strong>, or <strong data-start=\"878\" data-end=\"889\">no mode<\/strong> (if all numbers appear equally).<\/li>\n<\/ul>\n<h3 data-start=\"926\" data-end=\"962\"><strong data-start=\"930\" data-end=\"960\">Range &amp; Standard Deviation<\/strong><\/h3>\n<ul data-start=\"963\" data-end=\"1388\">\n<li data-start=\"963\" data-end=\"1011\"><strong data-start=\"965\" data-end=\"974\">Range<\/strong> = Largest number \u2013 Smallest number<\/li>\n<li data-start=\"1012\" data-end=\"1388\"><strong data-start=\"1014\" data-end=\"1041\">Standard Deviation (SD)<\/strong>:\n<ul data-start=\"1047\" data-end=\"1388\">\n<li data-start=\"1047\" data-end=\"1094\">Measures how far numbers are from the mean.<\/li>\n<li data-start=\"1097\" data-end=\"1162\">Larger SD means more spread; smaller SD means more clustered.<\/li>\n<li data-start=\"1165\" data-end=\"1260\"><strong data-start=\"1167\" data-end=\"1258\">If all numbers in a set are increased\/decreased by the same value, SD remains the same.<\/strong><\/li>\n<li data-start=\"1263\" data-end=\"1388\"><strong data-start=\"1265\" data-end=\"1386\">If all numbers are multiplied\/divided by a constant, SD is multiplied\/divided by the absolute value of that constant.<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3 data-start=\"1390\" data-end=\"1435\"><strong data-start=\"1394\" data-end=\"1435\">Quartiles &amp; Interquartile Range (IQR)<\/strong><\/h3>\n<ul data-start=\"1436\" data-end=\"1636\">\n<li data-start=\"1436\" data-end=\"1498\"><strong data-start=\"1438\" data-end=\"1461\">Q1 (First Quartile)<\/strong>: Median of the lower half of data.<\/li>\n<li data-start=\"1499\" data-end=\"1561\"><strong data-start=\"1501\" data-end=\"1524\">Q3 (Third Quartile)<\/strong>: Median of the upper half of data.<\/li>\n<li data-start=\"1562\" data-end=\"1636\"><strong data-start=\"1564\" data-end=\"1581\">IQR = Q3 &#8211; Q1<\/strong> (Measures the spread of the middle 50% of the data).<\/li>\n<\/ul>\n<h2 data-start=\"1643\" data-end=\"1686\"><strong data-start=\"1646\" data-end=\"1684\">2. Combinatorics Concepts for GMAT<\/strong><\/h2>\n<h3 data-start=\"1688\" data-end=\"1728\"><strong data-start=\"1692\" data-end=\"1726\">Fundamental Counting Principle<\/strong><\/h3>\n<ul data-start=\"1729\" data-end=\"1884\">\n<li data-start=\"1729\" data-end=\"1884\">If one event can happen in <strong data-start=\"1758\" data-end=\"1763\">m<\/strong> ways and another independent event can happen in <strong data-start=\"1813\" data-end=\"1818\">n<\/strong> ways, the total number of outcomes is: <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">m\u00d7nm \\times n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"1886\" data-end=\"1925\"><strong data-start=\"1890\" data-end=\"1923\">Permutations (Order Matters!)<\/strong><\/h3>\n<ul data-start=\"1926\" data-end=\"2484\">\n<li data-start=\"1926\" data-end=\"1994\">\n<p data-start=\"1928\" data-end=\"1994\">Used when order <strong data-start=\"1944\" data-end=\"1955\">matters<\/strong> (e.g., rankings, seat arrangements).<\/p>\n<\/li>\n<li data-start=\"1995\" data-end=\"2154\">\n<p data-start=\"1997\" data-end=\"2044\">Formula for <strong data-start=\"2009\" data-end=\"2041\">arranging n distinct objects<\/strong>:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">P(n,r)=n!(n\u2212r)!P(n, r) = \\frac{n!}{(n-r)!}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">r<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">r<\/span><span class=\"mclose\">)!<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">!<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"2089\" data-end=\"2095\">Where:<\/p>\n<ul data-start=\"2098\" data-end=\"2154\">\n<li data-start=\"2098\" data-end=\"2124\"><strong data-start=\"2100\" data-end=\"2105\">n<\/strong> = Total elements<\/li>\n<li data-start=\"2127\" data-end=\"2154\"><strong data-start=\"2129\" data-end=\"2134\">r<\/strong> = Chosen elements<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"2156\" data-end=\"2215\">\n<p data-start=\"2158\" data-end=\"2198\">Special case: <strong data-start=\"2172\" data-end=\"2195\">Arranging n objects<\/strong>:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">n!n!<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">!<\/span><\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"2217\" data-end=\"2484\">\n<p data-start=\"2219\" data-end=\"2313\"><strong data-start=\"2219\" data-end=\"2248\">Arranging with repetition<\/strong>:<br data-start=\"2249\" data-end=\"2252\" \/><br \/>\nIf there are <strong data-start=\"2267\" data-end=\"2272\">n<\/strong> objects where some are identical, use:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">n!k1!\u00d7k2!\u00d7\u2026\\frac{n!}{k_1! \\times k_2! \\times \\dots}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">k<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"mclose\">!<\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mord mathnormal\">k<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"mclose\">!<\/span><span class=\"mbin\">\u00d7<\/span><span class=\"minner\">\u2026<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">!<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"2371\" data-end=\"2449\">Example: Arranging the word <strong data-start=\"2399\" data-end=\"2414\">MISSISSIPPI<\/strong> (11 letters: M=1, I=4, S=4, P=2)<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">11!1!4!4!2!\\frac{11!}{1!4!4!2!}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">1<span class=\"mclose\">!<\/span>4<span class=\"mclose\">!<\/span>4<span class=\"mclose\">!<\/span>2<span class=\"mclose\">!<\/span>11<span class=\"mclose\">!<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"2486\" data-end=\"2532\"><strong data-start=\"2490\" data-end=\"2530\">Combinations (Order Doesn\u2019t Matter!)<\/strong><\/h3>\n<ul data-start=\"2533\" data-end=\"2782\">\n<li data-start=\"2533\" data-end=\"2603\">\n<p data-start=\"2535\" data-end=\"2603\">Used when order <strong data-start=\"2551\" data-end=\"2570\">does not matter<\/strong> (e.g., selecting a committee).<\/p>\n<\/li>\n<li data-start=\"2604\" data-end=\"2660\">\n<p data-start=\"2606\" data-end=\"2616\">Formula:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">C(n,r)=n!r!(n\u2212r)!C(n, r) = \\frac{n!}{r!(n-r)!}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">r<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">r<\/span><span class=\"mclose\">!<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span><span class=\"mord mathnormal\">r<\/span><span class=\"mclose\">)!<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mclose\">!<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"2662\" data-end=\"2782\">\n<p data-start=\"2664\" data-end=\"2716\"><strong data-start=\"2664\" data-end=\"2676\">Example:<\/strong> Choosing <strong data-start=\"2686\" data-end=\"2691\">3<\/strong> out of <strong data-start=\"2699\" data-end=\"2704\">5<\/strong> students:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">C(5,3)=5!3!(5\u22123)!=5!3!2!=10C(5,3) = \\frac{5!}{3!(5-3)!} = \\frac{5!}{3!2!} = 10<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">5<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">3<span class=\"mclose\">!<\/span><span class=\"mopen\">(<\/span>5<span class=\"mbin\">\u2212<\/span>3<span class=\"mclose\">)!<\/span>5<span class=\"mclose\">!<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">3<span class=\"mclose\">!<\/span>2<span class=\"mclose\">!<\/span>5<span class=\"mclose\">!<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"2789\" data-end=\"2839\"><strong data-start=\"2792\" data-end=\"2837\">3. Advanced GMAT Combinatorics Strategies<\/strong><\/h3>\n<h3 data-start=\"2841\" data-end=\"2887\"><strong data-start=\"2845\" data-end=\"2885\">Combination vs. Permutation Shortcut<\/strong><\/h3>\n<ul data-start=\"2888\" data-end=\"2980\">\n<li data-start=\"2888\" data-end=\"2930\"><strong data-start=\"2890\" data-end=\"2928\">If order matters \u2192 Use permutation<\/strong><\/li>\n<li data-start=\"2931\" data-end=\"2980\"><strong data-start=\"2933\" data-end=\"2978\">If order doesn\u2019t matter \u2192 Use combination<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"2982\" data-end=\"3015\"><strong data-start=\"2986\" data-end=\"3013\">&#8220;At Least One&#8221; Problems<\/strong><\/h3>\n<ul data-start=\"3016\" data-end=\"3111\">\n<li data-start=\"3016\" data-end=\"3111\">Use the <strong data-start=\"3026\" data-end=\"3050\">complement principle<\/strong>: <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">P(at\u00a0least\u00a0one)=1\u2212P(none)\\text{P(at least one)} = 1 &#8211; \\text{P(none)}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord text\"><span class=\"mord\">P(at\u00a0least\u00a0one)<\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord text\"><span class=\"mord\">P(none)<\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"3113\" data-end=\"3144\"><strong data-start=\"3117\" data-end=\"3142\">Circular Arrangements<\/strong><\/h3>\n<ul data-start=\"3145\" data-end=\"3313\">\n<li data-start=\"3145\" data-end=\"3225\">\n<p data-start=\"3147\" data-end=\"3204\">Formula for <strong data-start=\"3159\" data-end=\"3184\">circular permutations<\/strong> of <strong data-start=\"3188\" data-end=\"3193\">n<\/strong> objects:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(n\u22121)!(n-1)!<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)!<\/span><\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"3227\" data-end=\"3313\">\n<p data-start=\"3229\" data-end=\"3281\"><strong data-start=\"3229\" data-end=\"3241\">Example:<\/strong> 6 people sit around a circular table:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(6\u22121)!=5!=120(6-1)! = 5! = 120<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">6<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><span class=\"mclose\">)!<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mclose\">!<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">120<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"3315\" data-end=\"3355\"><strong data-start=\"3319\" data-end=\"3353\">Combinations with Restrictions<\/strong><\/h3>\n<ul data-start=\"3356\" data-end=\"3555\">\n<li data-start=\"3356\" data-end=\"3458\">If a certain person <strong data-start=\"3378\" data-end=\"3386\">must<\/strong> be included: First select that person, then choose the rest normally.<\/li>\n<li data-start=\"3459\" data-end=\"3555\">If a certain person <strong data-start=\"3481\" data-end=\"3491\">cannot<\/strong> be included: Exclude that person first, then choose the rest.<\/li>\n<\/ul>\n<h3 data-start=\"3562\" data-end=\"3619\"><strong data-start=\"3565\" data-end=\"3617\">4. GMAT Probability &amp; Overlap with Combinatorics<\/strong><\/h3>\n<h3 data-start=\"3621\" data-end=\"3650\"><strong data-start=\"3625\" data-end=\"3648\">Probability Formula<\/strong><\/h3>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">Probability=Favorable\u00a0OutcomesTotal\u00a0Outcomes\\text{Probability} = \\frac{\\text{Favorable Outcomes}}{\\text{Total Outcomes}}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord text\"><span class=\"mord\">Probability<\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord text\">Total\u00a0Outcomes<\/span><span class=\"mord text\">Favorable\u00a0Outcomes<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 data-start=\"3737\" data-end=\"3782\"><strong data-start=\"3741\" data-end=\"3780\">&#8220;Or&#8221; vs. &#8220;And&#8221; Rules in Probability<\/strong><\/h3>\n<ul data-start=\"3783\" data-end=\"3992\">\n<li data-start=\"3783\" data-end=\"3890\"><strong data-start=\"3785\" data-end=\"3835\">AND (Multiplication Rule, Independent Events):<\/strong> <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">P(A\u00a0and\u00a0B)=P(A)\u00d7P(B)P(A \\text{ and } B) = P(A) \\times P(B)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord text\"><span class=\"mord\">\u00a0and\u00a0<\/span><\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"3891\" data-end=\"3992\"><strong data-start=\"3893\" data-end=\"3943\">OR (Addition Rule, Mutually Exclusive Events):<\/strong> <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">P(A\u00a0or\u00a0B)=P(A)+P(B)P(A \\text{ or } B) = P(A) + P(B)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord text\"><span class=\"mord\">\u00a0or\u00a0<\/span><\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n<h3 data-start=\"3994\" data-end=\"4051\"><strong data-start=\"3998\" data-end=\"4049\">Binomial Probability (Rarely Tested but Useful)<\/strong><\/h3>\n<ul data-start=\"4052\" data-end=\"4291\">\n<li data-start=\"4052\" data-end=\"4291\">If each trial has two outcomes (Success, Failure), use <strong data-start=\"4109\" data-end=\"4134\">Binomial Distribution<\/strong>: <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">P(k)=C(n,k)pk(1\u2212p)n\u2212kP(k) = C(n, k) p^k (1-p)^{n-k}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">k<\/span><span class=\"mclose\">)<\/span><span class=\"mord\"><span class=\"mord mathnormal\">p<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mathnormal mtight\">k<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> Where:\n<ul data-start=\"4196\" data-end=\"4291\">\n<li data-start=\"4196\" data-end=\"4220\"><strong data-start=\"4198\" data-end=\"4203\">n<\/strong> = total trials<\/li>\n<li data-start=\"4223\" data-end=\"4254\"><strong data-start=\"4225\" data-end=\"4230\">k<\/strong> = number of successes<\/li>\n<li data-start=\"4257\" data-end=\"4291\"><strong data-start=\"4259\" data-end=\"4264\">p<\/strong> = probability of success<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3 data-start=\"4298\" data-end=\"4368\"><strong data-start=\"4301\" data-end=\"4366\">5. GMAT Test-Taking Strategies for Statistics &amp; Combinatorics<\/strong><\/h3>\n<p data-start=\"4369\" data-end=\"4818\">\u2705 <strong data-start=\"4371\" data-end=\"4396\">Memorize key formulas<\/strong> (especially permutations, combinations, and probability).<br data-start=\"4454\" data-end=\"4457\" \/><br \/>\n\u2705 <strong data-start=\"4459\" data-end=\"4488\">Use logic and elimination<\/strong>\u2014GMAT often provides unnecessary information to distract.<br data-start=\"4545\" data-end=\"4548\" \/><br \/>\n\u2705 <strong data-start=\"4550\" data-end=\"4579\">For probability questions<\/strong>, consider using <strong data-start=\"4596\" data-end=\"4617\">complement method<\/strong> to simplify calculations.<br data-start=\"4643\" data-end=\"4646\" \/><br \/>\n\u2705 <strong data-start=\"4648\" data-end=\"4681\">For complex counting problems<\/strong>, break them into smaller, manageable steps.<br data-start=\"4725\" data-end=\"4728\" \/><br \/>\n\u2705 <strong data-start=\"4730\" data-end=\"4767\">Use simple cases for verification<\/strong>\u2014If stuck, try smaller numbers to find a pattern.<\/p>\n<p data-start=\"4825\" data-end=\"4901\" data-is-last-node=\"\">Would you like additional practice problems or explanations on any topic?<\/p>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.manhattanreview.com\/download\/MR-GMAT-Quantitative-Question-Bank-BTG-D27-M8_07.11.2016.pdf\" target=\"_blank\" rel=\"noopener\">Turbocharge your GMAT: Quantitative Question Bank<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.dominatethegmat.com\/wp-content\/uploads\/2011\/01\/Math-Book-GMAT-Club.pdf\" target=\"_blank\" rel=\"noopener\">GMAT Club Math Book<\/a><\/h3>\n<h3 data-start=\"4825\" data-end=\"4901\"><a href=\"https:\/\/support.ebsco.com\/LEX\/501-GMAT-Questions.pdf\" target=\"_blank\" rel=\"noopener\">GMAT Statistics Combinatorics<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/bayanebartar.org\/file-dl\/library\/gmat\/gmat-for-dummies-7th-edition.pdf\" target=\"_blank\" rel=\"noopener\">gmat-for-dummies-7th-edition.pdf<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.manhattanreview.com\/download\/MR-GMAT-Quantitative-Question-Bank-BTG-D27-M8_23.01.2018.pdf\" target=\"_blank\" rel=\"noopener\">Turbocharge your GMAT: Quantitative Question Bank<\/a><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Author: Brian Galvin Size of File: 13MB Number Of Pages: 297 Language: English Category : GMAT Page Quality: Good GMAT Statistics Combinatorics Notes Download Link Here\u2019s a structured guide on GMAT Statistics &amp; Combinatorics to help you master these concepts efficiently. GMAT Statistics &amp; Combinatorics Strategy Guide 1. Statistics Concepts for GMAT Mean (Average) Formula: [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[476],"tags":[474,475],"class_list":["post-4759","post","type-post","status-publish","format-standard","hentry","category-gmat-statistics-combinatorics","tag-gmat-statistics","tag-gmat-statistics-combinatorics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts\/4759","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/users\/53"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/comments?post=4759"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts\/4759\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/media?parent=4759"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/categories?post=4759"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/tags?post=4759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}