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GATE Permutation & Combination Questions with Answers & Explanations

20 Permutation & Combination questions from the Engineering Mathematics section of GATE, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

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Question 1

In how many ways can a committee of 2 be chosen from 10 people?

  1. A20
  2. B45
  3. C55
  4. D90
Show answer
Answer: (B) 45 ⁿCᵣ = 10C2 = 45.
Question 2

In how many ways can a committee of 2 be chosen from 9 people?

  1. A18
  2. B36
  3. C72
  4. D45
Show answer
Answer: (B) 36 ⁿCᵣ = 9C2 = 36.
Question 3

In how many ways can a committee of 2 be chosen from 6 people?

  1. A21
  2. B30
  3. C12
  4. D15
Show answer
Answer: (D) 15 ⁿCᵣ = 6C2 = 15.
Question 4

In how many ways can a committee of 4 be chosen from 6 people?

  1. A24
  2. B15
  3. C21
  4. D30
Show answer
Answer: (B) 15 ⁿCᵣ = 6C4 = 15.
Question 5

In how many ways can a committee of 4 be chosen from 8 people?

  1. A140
  2. B1680
  3. C70
  4. D78
Show answer
Answer: (C) 70 ⁿCᵣ = 8C4 = 70.
Question 6

In how many ways can a committee of 3 be chosen from 12 people?

  1. A440
  2. B232
  3. C220
  4. D36
Show answer
Answer: (C) 220 ⁿCᵣ = 12C3 = 220.
Question 7

In how many ways can a committee of 3 be chosen from 9 people?

  1. A93
  2. B168
  3. C504
  4. D84
Show answer
Answer: (D) 84 ⁿCᵣ = 9C3 = 84.
Question 8

In how many ways can a committee of 4 be chosen from 12 people?

  1. A495
  2. B507
  3. C11880
  4. D48
Show answer
Answer: (A) 495 ⁿCᵣ = 12C4 = 495.
Question 9

In how many ways can a committee of 3 be chosen from 10 people?

  1. A720
  2. B120
  3. C240
  4. D130
Show answer
Answer: (B) 120 ⁿCᵣ = 10C3 = 120.
Question 10

In how many ways can a committee of 2 be chosen from 7 people?

  1. A42
  2. B21
  3. C28
  4. D14
Show answer
Answer: (B) 21 ⁿCᵣ = 7C2 = 21.

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Question 11

In how many ways can a committee of 3 be chosen from 6 people?

  1. A120
  2. B18
  3. C40
  4. D20
Show answer
Answer: (D) 20 ⁿCᵣ = 6C3 = 20.
Question 12

In how many ways can a committee of 4 be chosen from 7 people?

  1. A42
  2. B840
  3. C70
  4. D35
Show answer
Answer: (D) 35 ⁿCᵣ = 7C4 = 35.
Question 13

In how many ways can a committee of 2 be chosen from 8 people?

  1. A16
  2. B36
  3. C56
  4. D28
Show answer
Answer: (D) 28 ⁿCᵣ = 8C2 = 28.
Question 14

In how many ways can a committee of 3 be chosen from 7 people?

  1. A35
  2. B21
  3. C42
  4. D70
Show answer
Answer: (A) 35 ⁿCᵣ = 7C3 = 35.
Question 15

In how many ways can a committee of 4 be chosen from 9 people?

  1. A126
  2. B252
  3. C36
  4. D135
Show answer
Answer: (A) 126 ⁿCᵣ = 9C4 = 126.
Question 16

In how many ways can a committee of 2 be chosen from 10 people?

  1. A90
  2. B55
  3. C45
  4. D20
Show answer
Answer: (C) 45 ⁿCᵣ = 10C2 = 45.
Question 17

In how many ways can a committee of 2 be chosen from 11 people?

  1. A110
  2. B22
  3. C66
  4. D55
Show answer
Answer: (D) 55 ⁿCᵣ = 11C2 = 55.
Question 18

In how many ways can a committee of 4 be chosen from 7 people?

  1. A70
  2. B35
  3. C42
  4. D28
Show answer
Answer: (B) 35 ⁿCᵣ = 7C4 = 35.
Question 19

In how many ways can a committee of 3 be chosen from 11 people?

  1. A176
  2. B33
  3. C990
  4. D165
Show answer
Answer: (D) 165 ⁿCᵣ = 11C3 = 165.
Question 20

In how many ways can a committee of 3 be chosen from 8 people?

  1. A64
  2. B336
  3. C56
  4. D24
Show answer
Answer: (C) 56 ⁿCᵣ = 8C3 = 56.

These are RankerClub practice questions written in the GATE pattern. They are not official SSC/IBPS/RRB papers.

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