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Quantitative practice

Permutations and Combinations Questions with Answers

Counting arrangements where order matters and selections where it does not. This page pools every permutations and combinations question on the site (129 of them, from 38 exams, weighted towards Engineering, Management, University & Science) so you can drill the topic on its own instead of meeting four of them inside a full paper.

40% of the pool is graded hard on this site’s own scale and 15% easy, which is harder than the average topic in this section.

Questions
129
Practice set
25 in 25 min
Difficulty
19/58/52
Negative marking
None
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Permutations and Combinations questions with solutions

6 from the 129-question pool, worked in full.

  1. 1. How many 3-letter arrangements can be made from A,B,C,D without repetition?

    • A. 12
    • B. 4
    • C. 24 ✓
    • D. 64

    Solution. The number is 4P3=4x3x2=24.

  2. 2. Three integers are chosen from the set {1,2,3,4,5,6,7,8}. The number of choices whose sum is even is

    • A. 28 ✓
    • B. 24
    • C. 32
    • D. 36

    Solution. An even sum occurs either when all three chosen integers are even, or when exactly two are odd and one is even. There are 4 even and 4 odd integers. Hence the count is C(4,3)+C(4,2)C(4,1)=4+24=28.

  3. 3. Seven distinct runners P, Q, R, S, T, U and V stand in a line. P must be somewhere to the left of Q, while R and S must not stand next to each other. The number of possible lineups is

    • A. 1440
    • B. 1800 ✓
    • C. 2160
    • D. 2520

    Solution. Exactly half of all 7! lineups have P left of Q, giving 2520. If R and S are adjacent, treat them as a block: 6!×2 lineups, of which half have P left of Q, giving 720. Hence 2520-720=1800.

  4. 4. Using the digits 0,1,2,3,4,5 without repetition, how many five-digit even numbers can be formed?

    Solution. Count by the last digit. If the last digit is 0, the first digit has 5 choices and the middle three positions have P(4,3)=24 choices: 120. If the last digit is 2 or 4, choose the last digit in 2 ways, the first digit from the 4 non-zero remaining digits, and arrange 3 of the remaining 4 digits: 2×4×P(4,3)=192. Total=312.

  5. 5. The number of ways to arrange 4 distinct books on a shelf is:

    • A. 4
    • B. 12
    • C. 24 ✓
    • D. 16

    Solution. 4!=24.

  6. 6. How many 3-member committees can be chosen from 7 people?

    • A. 21
    • B. 42
    • C. 210
    • D. 35 ✓

    Solution. The number is C(7,3)=7x6x5/(3x2x1)=35.

Exams that set Permutations and Combinations

3 categories, led by Engineering, Management, University & Science.

    Drawn from AEEE, AMU B.Tech., AP EAPCET, Assam CEE, ATIT, ATMA, BCECE, BV-BTECH, CAT, CG PET, COMEDK UGET, CUCET, CUSAT CAT, IBSAT, IEMJEE, IMU-CET, IPMAT Indore, JAIN JET, JEE Advanced, JEE Main, JEE Main Paper 2, KCET, Kerala MCA, KIITEE, KLEEE, MET, MHT CET, NERIST NEE, NMAT, OJEE, SAEEE, SITEEE, SNAP, SRMJEEE, TG EAPCET, TJEE, UPESEAT, VITEEE.

    Permutations and Combinations: frequently asked questions

    How many permutations and combinations questions are there?

    129, from the 38 exams here whose syllabus sets the topic. 15% are graded easy and 40% hard, which makes permutations and combinations one of the harder topics in this section, against a 18% average.

    Which exams ask permutations and combinations questions?

    38 of the exams on this site, weighted towards Engineering (31), Management (6), University & Science (1). Every question in this pool comes from one of their own mock tests, so the list below is the honest answer to whether the topic is worth your time.

    Is permutations and combinations hard?

    40% of these 129 questions are graded hard and 15% easy, making it one of the harder topics in this section, against a 18% average.

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