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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 — 118 of them, from 37 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.

36% of the pool is graded hard on this site’s own scale and 16% easy, which is harder than the average topic in this section.

Questions
118
Practice set
25 in 25 min
Difficulty
19/56/43
Negative marking
None
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Permutations and Combinations questions with solutions

6 from the 118-question pool, worked in full.

  1. 1. The number of ways to choose 4 vertices of a regular 12-gon so that no two chosen vertices are adjacent is

    • A. 96
    • B. 105 ✓
    • C. 108
    • D. 120

    Solution. For k nonadjacent choices on a cycle of n labeled positions, the count is n/(n-k) C(n-k,k). With n=12 and k=4, the number is 12/8 x C(8,4)=3/2 x 70=105.

  2. 2. Five distinct men and four distinct women are arranged in a row so that no two women are adjacent. The number of such arrangements is

    • A. 28800
    • B. 14400
    • C. 86400
    • D. 43200 ✓

    Solution. Arrange the 5 men in 5! ways. This creates 6 gaps. Choose and order 4 of these gaps for the women in P(6,4)=6×5×4×3 ways. Total =5!×P(6,4)=120×360=43200.

  3. 3. How many 5-letter arrangements can be formed from the letters of PLANET if the arrangement must begin with a vowel and no letter is repeated?

    • A. 120
    • B. 240 ✓
    • C. 480
    • D. 360

    Solution. PLANET has two vowels, A and E. Choose the first letter in 2 ways, then arrange 4 of the remaining 5 letters in P(5,4)=120 ways. Total=2×120=240.

  4. 4. Six distinct men and four distinct women are seated around a circular table so that no two women are adjacent. The number of arrangements is

    • A. 21600
    • B. 17280
    • C. 86400
    • D. 43200 ✓

    Solution. Arrange the six men around the circle in 5! ways. Choose four of the six gaps for the women and arrange the four women: 5! C(6,4) 4! =120x15x24=43200.

  5. 5. How many 4-digit numbers can be formed from digits 1,2,3,4,5 without repetition and greater than 3000?

    • A. 120
    • B. 48
    • C. 72 ✓
    • D. 60

    Solution. The thousands digit can be 3,4 or5: 3 choices. Remaining three positions are 4P3=24, so total 72.

  6. 6. The number of permutations of {1,2,3,4,5,6,7} in which 1 and 2 occupy positions differing by exactly 3 and 3 appears before 4 is

    Solution. For 1 and 2 to occupy positions differing by 3, their unordered position pair can be (1,4),(2,5),(3,6) or (4,7): 4 choices. Assign 1 and 2 to the chosen positions in 2 ways, and arrange the remaining five numbers in 5! ways, giving 4x2x120=960 permutations. Swapping labels 3 and 4 pairs these permutations without affecting the positions of 1 and 2, so exactly half have 3 before 4. The answer is 480.

Exams that set Permutations and Combinations

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

Also set by 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. Browse all exams.

Permutations and Combinations: frequently asked questions

How many permutations and combinations questions are there?

118, from the 37 exams here whose syllabus sets the topic. 16% are graded easy and 36% 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?

37 of the exams on this site, weighted towards Engineering (30), 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?

36% of these 118 questions are graded hard and 16% easy, making it one of the harder topics in this section, against a 17% average.

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