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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 (137 of them, from 42 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.

39% of the pool is graded hard on this site’s own scale and 14% easy, which is harder than the average topic in this section.

Questions
137
Practice set
25 in 25 min
Difficulty
19/65/53
Negative marking
None
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Permutations and Combinations questions with solutions

6 from the 137-question pool, worked in full.

  1. 1. The number of diagonals in a regular 12-gon is

    • A. 60
    • B. 66
    • C. 48
    • D. 54 ✓

    Solution. Each pair of vertices determines a segment, giving C(12,2)=66. Removing the 12 sides leaves 66-12=54 diagonals.

  2. 2. 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.

  3. 3. The number of ways to arrange 3 books out of 5 distinct books on a shelf is

    • A. 15
    • B. 20
    • C. 125
    • D. 60 ✓

    Solution. P(5,3) = 5!/(5-3)! = 5x4x3 = 60.

  4. 4. How many distinct arrangements can be made using all the letters of the word 'LEVEL'?

    • A. 120
    • B. 30 ✓
    • C. 20
    • D. 60

    Solution. LEVEL has 5 letters with L repeated twice and E repeated twice, so arrangements=5!/(2!2!)=120/4=30.

  5. 5. How many distinct arrangements are possible for the letters of BANANA?

    • A. 120
    • B. 720
    • C. 180
    • D. 60 ✓

    Solution. BANANA has 6 letters with A repeated 3 times and N repeated twice, so 6!/(3!2!)=60.

  6. 6. Six distinct books are placed on a shelf. In how many arrangements are two specified books not adjacent?

    • A. 360
    • B. 600
    • C. 480 ✓
    • D. 240

    Solution. Total arrangements 6!=720. Adjacent arrangements: treat the pair as one block, giving 5!*2=240. Hence nonadjacent arrangements=480.

Exams that set Permutations and Combinations

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

Also set by CUSAT CAT, IBSAT, IEMJEE, IMU-CET, IPMAT Indore, IPMAT Rohtak, JAIN JET, JEE Advanced, JEE Main, JEE Main Paper 2, KCET, Kerala MCA, KIITEE, KLEEE, MET, MHT CET, NDA, NERIST NEE, NMAT, OJEE, SAEEE, SITEEE, SNAP, SRMJEEE, TG EAPCET, TJEE, UPESEAT, VITEEE, XAT, JAMB UTME. Browse all exams.

Permutations and Combinations: frequently asked questions

How many permutations and combinations questions are there?

137, from the 42 exams here whose syllabus sets the topic. 14% are graded easy and 39% hard, which makes permutations and combinations one of the harder topics in this section, against a 17% average.

Which exams ask permutations and combinations questions?

42 of the exams on this site, weighted towards Engineering (31), Management (8), University & Science (2). 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?

39% of these 137 questions are graded hard and 14% easy, making it one of the harder topics in this section, against a 17% average.

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