{"id":5829,"date":"2026-10-17T11:11:40","date_gmt":"2026-10-17T05:41:40","guid":{"rendered":"https:\/\/www.catmock.com\/blog\/?p=5829"},"modified":"2026-10-17T11:11:41","modified_gmt":"2026-10-17T05:41:41","slug":"xat-2027-quantitative-aptitude-probability-permutation-questions","status":"publish","type":"post","link":"https:\/\/www.catmock.com\/blog\/xat-2027-quantitative-aptitude-probability-permutation-questions\/","title":{"rendered":"XAT 2027 Quantitative Aptitude: How to Solve Probability and Permutation Questions"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">You glance at an XAT quant question: <em>\u201cFive people are to be seated in a row, and two of them refuse to sit apart\u2026\u201d<\/em> Your mind freezes. Is it a permutation? A combination? Do you multiply, add or divide? Many aspirants lose precious minutes at exactly this point, not because the maths is hard, but because they cannot decide <em>which tool to pick<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This guide fixes that. Whether you are an aspirant in the final stretch or just starting your <strong>XAT 2027 Quantitative Aptitude<\/strong> preparation, you will learn a clear decision process, the formulas that matter, ten fully solved questions and a four-week plan. The goal is simple: make probability and permutation questions feel predictable.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Why Probability and Permutation Matter in XAT 2027<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Several preparation reviews point to the same fact: the Quantitative Ability and Data Interpretation (QADI) block is the largest in Part 1, with around 28 questions, and Modern Math topics such as <strong>probability, permutation and combination, and set theory<\/strong> are repeatedly flagged as high-priority areas. XAT is conducted by XLRI Jamshedpur, and the <a href=\"https:\/\/xatonline.in\">official XAT website<\/a> publishes the notification, so always confirm the latest dates and exam pattern there. Current reports place XAT 2027 on <strong>3 January 2027<\/strong>, but treat that as a date to verify.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here is why this chapter pays off:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>It is conceptual, not calculation-heavy.<\/strong> One clear idea often replaces a page of working.<\/li>\n\n\n\n<li><strong>XAT likes application.<\/strong> Questions are wrapped in real-world situations rather than plain formula drills.<\/li>\n\n\n\n<li><strong>It links to other topics.<\/strong> Counting skills help in set theory, DI and even logic-based decision-making questions.<\/li>\n\n\n\n<li><strong>It is learnable fast.<\/strong> A small toolkit covers a very large share of questions.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Permutation vs Combination: Master the Difference First<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Before any formula, answer one question: <strong>Does the order matter?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If <strong>order matters<\/strong> (arranging, ranking, forming words or numbers, seating), use a <strong>permutation<\/strong>.<\/li>\n\n\n\n<li>If <strong>order does not matter<\/strong> (selecting, choosing, forming a committee or team), use a <strong>combination<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">A simple memory aid: a <em>combination lock<\/em> is really a <em>permutation lock<\/em>, because the order of digits matters. Keep that joke in mind and you will not mix them up. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Table 1: Essential Counting Formulas for XAT<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Situation<\/th><th>Formula<\/th><th>Example use<\/th><\/tr><\/thead><tbody><tr><td>Fundamental counting principle<\/td><td>m \u00d7 n (steps in sequence)<\/td><td>Outfits from shirts and trousers<\/td><\/tr><tr><td>Arranging n distinct objects<\/td><td>n!<\/td><td>Seating in a row<\/td><\/tr><tr><td>Arranging r of n objects<\/td><td>\u207fP\u1d63 = n!\/(n \u2212 r)!<\/td><td>Forming 3-letter codes<\/td><\/tr><tr><td>Choosing r of n objects<\/td><td>\u207fC\u1d63 = n!\/(r!(n \u2212 r)!)<\/td><td>Selecting a committee<\/td><\/tr><tr><td>Identical objects present<\/td><td>n!\/(p! q! r!)<\/td><td>Letters of BANANA<\/td><\/tr><tr><td>Circular arrangement<\/td><td>(n \u2212 1)!<\/td><td>People around a round table<\/td><\/tr><tr><td>Distribution (non-negative)<\/td><td>\u207f\u207a\u02b3\u207b\u00b9C\u1d63<\/td><td>Dividing identical items among people<\/td><\/tr><tr><td>Distribution (each at least 1)<\/td><td>\u207f\u207b\u00b9C\u1d63\u208b\u2081<\/td><td>Each person gets at least one<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The distribution rows come from the \u201cstars and bars\u201d method. They appear often in XAT-style questions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">The 5-Step Method for Any Counting Question<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Use this sequence every time:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Define the objects.<\/strong> Are they distinct or identical?<\/li>\n\n\n\n<li><strong>Check the order.<\/strong> Does the arrangement matter (permutation) or only the selection (combination)?<\/li>\n\n\n\n<li><strong>Spot restrictions.<\/strong> Words like \u201ctogether\u201d, \u201cnot together\u201d, \u201cat least\u201d, \u201cexactly\u201d and \u201cadjacent\u201d change the method.<\/li>\n\n\n\n<li><strong>Choose a strategy.<\/strong> Direct counting, <strong>complement<\/strong> (total \u2212 unwanted), or <strong>block method<\/strong>.<\/li>\n\n\n\n<li><strong>Sense-check.<\/strong> Is the answer smaller than the total possible outcomes? Is it a whole number?<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Solving Permutation Questions: Worked Examples<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Example 1: Arrangements with a \u201cTogether\u201d Condition<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> In how many ways can the letters of the word XAVIER be arranged so that the three vowels A, I and E are <strong>not<\/strong> all together?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total arrangements (all letters distinct) = 6! = 720<\/li>\n\n\n\n<li>Treat A, I, E as one block: the block plus X, V and R makes 4 units, so 4! = 24 ways<\/li>\n\n\n\n<li>Inside the block, the vowels can be arranged in 3! = 6 ways<\/li>\n\n\n\n<li>Together = 24 \u00d7 6 = 144<\/li>\n\n\n\n<li><strong>Not together = 720 \u2212 144 = 576<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Lesson:<\/strong> \u201cNot together\u201d is almost always solved by the <strong>complement method<\/strong>: count everything, subtract the \u201ctogether\u201d case.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example 2: Circular Arrangement<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> Six people sit around a round table. In how many ways can they sit if two particular people must sit together?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Treat the pair as one block: 5 units around the table = (5 \u2212 1)! = 24<\/li>\n\n\n\n<li>The pair can swap places: 2 ways<\/li>\n\n\n\n<li><strong>Total = 24 \u00d7 2 = 48<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Follow-up:<\/strong> If the two must <strong>not<\/strong> sit together, the answer is 5! \u2212 48 = 120 \u2212 48 = <strong>72<\/strong>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example 3: Forming Numbers with a Condition<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> How many even four-digit numbers can be formed from the digits 1, 2, 3, 4, 5 without repetition?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fill the <strong>restricted position first<\/strong>. The units digit must be 2 or 4, so there are 2 choices.<\/li>\n\n\n\n<li>The remaining three places use the other four digits: 4 \u00d7 3 \u00d7 2 = 24 ways<\/li>\n\n\n\n<li><strong>Total = 2 \u00d7 24 = 48<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Lesson:<\/strong> Always fill the <strong>restricted place first<\/strong>. This avoids messy subtraction later.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example 4: Distribution Question<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> How many non-negative integer solutions does x + y + z = 10 have?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use \u207f\u207a\u02b3\u207b\u00b9C\u1d63 with n = 3 variables and r = 10<\/li>\n\n\n\n<li>\u00b9\u00b2C\u2082 = 66<\/li>\n\n\n\n<li><strong>Answer: 66<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">If each variable must be <strong>at least 1<\/strong>, use \u2079C\u2082 = <strong>36<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solving Combination (Selection) Questions<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Example 5: \u201cAt Least\u201d Selection<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> A committee of 4 is chosen from 6 men and 4 women. In how many ways can it have <strong>at least 2 women<\/strong>?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution (complement method):<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total committees = \u00b9\u2070C\u2084 = 210<\/li>\n\n\n\n<li>Fewer than 2 women means 0 or 1 woman:\n<ul class=\"wp-block-list\">\n<li>0 women: \u2076C\u2084 = 15<\/li>\n\n\n\n<li>1 woman: \u2074C\u2081 \u00d7 \u2076C\u2083 = 4 \u00d7 20 = 80<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>At least 2 women = 210 \u2212 (15 + 80) = 115<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Check by direct counting:<\/strong> 2 women (90) + 3 women (24) + 4 women (1) = 115 \u2713<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Lesson:<\/strong> \u201cAt least\u201d and \u201cat most\u201d are hints to use the <strong>complement<\/strong> when the opposite case has fewer terms.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Decision Guide: Which Tool Should You Use?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Table 2: Clue Words and the Method They Suggest<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Clue word or phrase<\/th><th>Meaning<\/th><th>Method<\/th><\/tr><\/thead><tbody><tr><td>\u201cArrange\u201d, \u201cseat\u201d, \u201crank\u201d, \u201cform words or numbers\u201d<\/td><td>Order matters<\/td><td>Permutation<\/td><\/tr><tr><td>\u201cSelect\u201d, \u201cchoose\u201d, \u201ccommittee\u201d, \u201cteam\u201d<\/td><td>Order does not matter<\/td><td>Combination<\/td><\/tr><tr><td>\u201cTogether\u201d, \u201cadjacent\u201d<\/td><td>Group acts as one unit<\/td><td>Block method<\/td><\/tr><tr><td>\u201cNot together\u201d, \u201cnot adjacent\u201d<\/td><td>Opposite of block<\/td><td>Total \u2212 together<\/td><\/tr><tr><td>\u201cAt least\u201d or \u201cat most\u201d<\/td><td>Many cases<\/td><td>Complement<\/td><\/tr><tr><td>\u201cIdentical\u201d, \u201csame type\u201d<\/td><td>Repeats exist<\/td><td>Divide by factorials<\/td><\/tr><tr><td>\u201cRound table\u201d, \u201cnecklace\u201d<\/td><td>Rotational symmetry<\/td><td>(n \u2212 1)!<\/td><\/tr><tr><td>\u201cDivide among\u201d, \u201cdistribute\u201d<\/td><td>Stars and bars<\/td><td>\u207f\u207a\u02b3\u207b\u00b9C\u1d63<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Probability: The Core Ideas<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Probability = Favourable outcomes \u00f7 Total outcomes<\/strong>, when all outcomes are equally likely. Another word for the same idea is <em>likelihood<\/em>. A probability is always between 0 and 1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Table 3: Probability Rules You Must Know<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Concept<\/th><th>Formula<\/th><th>When to use<\/th><\/tr><\/thead><tbody><tr><td>Basic probability<\/td><td>P(E) = favourable\/total<\/td><td>Equally likely outcomes<\/td><\/tr><tr><td>Complement<\/td><td>P(not E) = 1 \u2212 P(E)<\/td><td>\u201cAt least one\u201d questions<\/td><\/tr><tr><td>Addition rule<\/td><td>P(A or B) = P(A) + P(B) \u2212 P(A and B)<\/td><td>Either event happens<\/td><\/tr><tr><td>Independent events<\/td><td>P(A and B) = P(A) \u00d7 P(B)<\/td><td>Outcome of one does not affect the other<\/td><\/tr><tr><td>Conditional probability<\/td><td>P(A given B) = P(A and B)\/P(B)<\/td><td>Information about B is given<\/td><\/tr><tr><td>Without replacement<\/td><td>Multiply with reduced totals<\/td><td>Cards, balls, draws<\/td><\/tr><tr><td>Expected value<\/td><td>\u03a3 (value \u00d7 probability)<\/td><td>Games, gains and losses<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Solving Probability Questions: Worked Examples<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Example 6: Dice and Sample Space<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> Two fair dice are rolled. What is the probability that the sum is 8?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Favourable outcomes: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5<\/li>\n\n\n\n<li>Total outcomes = 36<\/li>\n\n\n\n<li><strong>Probability = 5\/36<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Example 7: The \u201cAt Least One\u201d Shortcut<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> A fair coin is tossed 4 times. What is the probability of getting <strong>at least one head<\/strong>?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(no heads) = (1\/2)\u2074 = 1\/16<\/li>\n\n\n\n<li><strong>P(at least one head) = 1 \u2212 1\/16 = 15\/16<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Lesson:<\/strong> Whenever you see \u201cat least one\u201d, think <strong>1 \u2212 P(none)<\/strong>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example 8: Drawing Without Replacement<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> Two cards are drawn one after another, without replacement, from a standard deck. What is the probability that both are aces?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First ace: 4\/52<\/li>\n\n\n\n<li>Second ace: 3\/51<\/li>\n\n\n\n<li><strong>Probability = (4\/52) \u00d7 (3\/51) = 12\/2652 = 1\/221<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Example 9: Conditional Probability<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> A family has two children. Given that <strong>at least one is a boy<\/strong>, what is the probability that both are boys?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Possible families: BB, BG, GB, GG<\/li>\n\n\n\n<li>\u201cAt least one boy\u201d removes GG, leaving BB, BG, GB (3 outcomes)<\/li>\n\n\n\n<li>Only BB has both boys<\/li>\n\n\n\n<li><strong>Probability = 1\/3<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Common trap:<\/strong> Many candidates answer 1\/2. The word <em>given<\/em> shrinks the sample space, so always rewrite the sample space after the condition.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example 10: Permutation Meets Probability<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> Five people, including A and B, are arranged randomly in a row. What is the probability that A and B stand next to each other?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total arrangements = 5! = 120<\/li>\n\n\n\n<li>Favourable: treat A and B as a block, giving 4! = 24 arrangements, times 2 for their internal order = 48<\/li>\n\n\n\n<li><strong>Probability = 48\/120 = 2\/5<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Lesson:<\/strong> Many XAT questions are really counting problems wearing a probability costume. Count favourable and total outcomes with the same tools.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Bonus: Expected Value<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> You roll a fair die. If an even number appears, you win that amount in rupees. If an odd number appears, you lose \u20b93. What is your expected gain?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Gains: (2 + 4 + 6)\/6 = 12\/6 = 2<\/li>\n\n\n\n<li>Losses: 3 \u00d7 3\/6 = 9\/6 = 1.5<\/li>\n\n\n\n<li><strong>Expected value = 2 \u2212 1.5 = \u20b90.50<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Common Mistakes That Cost Marks<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Confusing order and selection.<\/strong> This is the number one error. Ask \u201cdoes order matter?\u201d every time.<\/li>\n\n\n\n<li><strong>Forgetting internal arrangements in a block.<\/strong> The pair can swap, so multiply by 2.<\/li>\n\n\n\n<li><strong>Counting identical objects as distinct.<\/strong> Always divide by the factorial of repeats.<\/li>\n\n\n\n<li><strong>Ignoring the condition in \u201cgiven\u201d questions.<\/strong> Shrink the sample space first.<\/li>\n\n\n\n<li><strong>Mixing replacement and non-replacement.<\/strong> In non-replacement draws the denominator falls with each draw.<\/li>\n\n\n\n<li><strong>Overcounting with \u201cor\u201d.<\/strong> Subtract the overlap, as the addition rule says.<\/li>\n\n\n\n<li><strong>Skipping the sanity check.<\/strong> A probability above 1 means something is wrong.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to Manage Time and Attempts in XAT QADI<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">XAT rewards judgement. Not every question deserves your time. Here are practical rules:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Do the cleanest counting questions first.<\/strong> Direct, short setups give fast marks.<\/li>\n\n\n\n<li><strong>Attempt a question only if you can see the method in 30 seconds.<\/strong> Otherwise mark it and move on.<\/li>\n\n\n\n<li><strong>Skip heavy casework early.<\/strong> Return to it if time remains.<\/li>\n\n\n\n<li><strong>Check the official rules on unattempted questions and negative marking<\/strong> in the latest XAT notification, since these affect how many questions you should attempt. Never rely on old rules.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Your 4-Week Practice Plan for XAT 2027<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Table 4: Four-Week Plan for Probability and Permutation<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Week<\/th><th>Focus<\/th><th>Daily target<\/th><\/tr><\/thead><tbody><tr><td><strong>Week 1<\/strong><\/td><td>Counting principle, permutations, combinations; clue-word table<\/td><td>10\u201312 questions plus 1 revision of formulas<\/td><\/tr><tr><td><strong>Week 2<\/strong><\/td><td>Block method, circular arrangements, distributions, \u201cat least\u201d selection<\/td><td>10\u201312 questions, restrictions first<\/td><\/tr><tr><td><strong>Week 3<\/strong><\/td><td>Probability basics, complement, independent and conditional events, expected value<\/td><td>10 questions plus 1 timed mini-set<\/td><\/tr><tr><td><strong>Week 4<\/strong><\/td><td>Mixed XAT-style questions, previous-year papers and mock tests<\/td><td>1 timed QADI sectional plus error review<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Pro tips<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Keep a <strong>mistake log<\/strong> noting whether each error was in method, calculation or reading.<\/li>\n\n\n\n<li>Revise Tables 1 to 3 every weekend.<\/li>\n\n\n\n<li>Combine this chapter with XAT previous year quant questions and a full XAT mock test series.<\/li>\n\n\n\n<li>For related topics, read our guides on set theory and Venn diagrams for set and XAT Data Interpretation preparation.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Summary<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Probability, permutation and combination sit within XAT\u2019s Modern Math cluster and are repeatedly flagged as high-priority for XAT 2027.<\/li>\n\n\n\n<li><strong>Decide first: does order matter?<\/strong> Permutation if yes, combination if no.<\/li>\n\n\n\n<li>Use the <strong>block method<\/strong> for \u201ctogether\u201d, the <strong>complement<\/strong> for \u201cnot together\u201d and \u201cat least\u201d, and <strong>stars and bars<\/strong> for distributions.<\/li>\n\n\n\n<li>In probability, always define the <strong>sample space<\/strong>, shrink it for \u201cgiven\u201d questions, and use <strong>1 \u2212 P(none)<\/strong> for \u201cat least one\u201d.<\/li>\n\n\n\n<li>Many probability questions are counting questions in disguise.<\/li>\n\n\n\n<li>Build a mistake log and practise in four stages, from basics to timed mixed sets.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Frequently Asked Questions (FAQs)<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">1. Are probability and permutation questions important for XAT 2027?<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. Preparation reviews consistently list probability, permutation and combination among the high-priority Modern Math topics inside the QADI block, which has about 28 questions. Check the official XAT website for the latest pattern.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2. How do I know whether to use permutation or combination?<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Ask whether the order of the result matters. Arranging, ranking and forming numbers or words call for permutations. Selecting, choosing and forming committees or teams call for combinations.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">3. What is the fastest way to solve \u201cat least\u201d questions?<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Use the complement method. Count the total or find the probability of the opposite case, then subtract. For example, P(at least one) = 1 \u2212 P(none).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">4. Why do candidates get conditional probability wrong?<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">They forget that the \u201cgiven\u201d information shrinks the sample space. Rewrite the list of possible outcomes after applying the condition, then count the favourable ones within that smaller list.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">5. How many probability and permutation questions should I practise before XAT 2027?<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Aim for about 150 to 200 well-reviewed questions across basic, application and mixed levels. Quality matters more than quantity, so log every error and the reason behind it.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Probability and permutation questions reward the aspirant who asks the right first question: <em>Does order matter, and what are the restrictions?<\/em> Once you answer that, the rest is a short, predictable chain of steps. Block, complement, divide by repeats or shrink the sample space. That is the entire toolkit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Start with the formula table, work through the ten solved examples until the reasoning feels natural, and follow the four-week plan. By the time <strong>XAT 2027<\/strong> arrives, a counting question will look less like a trap and more like a reliable source of marks. Practise steadily, review honestly and walk in with confidence.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You May Also Like :\u00a0<strong><a href=\"https:\/\/www.catmock.com\/\">CAT MOCK<\/a><\/strong>,\u00a0<strong><a href=\"https:\/\/www.catmock.com\/pyq\/cat\/2017\">CAT MOCK PYQ<\/a><\/strong><br>Follow Us On :\u00a0<a href=\"https:\/\/www.facebook.com\/catmock.in?mibextid=ZbWKwL\"><strong>Facebook<\/strong><\/a>,\u00a0<strong><a href=\"https:\/\/www.instagram.com\/cat.mock\">Instagram<\/a><\/strong>,\u00a0<a href=\"https:\/\/www.youtube.com\/@CATMock\"><strong>Youtube<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>You glance at an XAT quant question: \u201cFive people are to be seated in a row, and two of them refuse to sit apart\u2026\u201d Your mind freezes. Is it a permutation? A combination? Do you multiply, add or divide? Many aspirants lose precious minutes at exactly this point, not because the maths is hard, but [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":5831,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ocean_front_end_style_editor":"no","ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"on","ocean_gallery_id":[],"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5829","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","entry","has-media"],"featured_image_src":"https:\/\/www.catmock.com\/blog\/wp-content\/uploads\/2026\/10\/XAT-2027-Probability-Permutations-Prep-1.webp","author_info":{"display_name":"Diya","author_link":"https:\/\/www.catmock.com\/blog\/author\/catmock\/"},"yoast_head":"<!-- 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