Permutation and Combination Questions and Answers

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Q21
From 6 men, a committee of 3 can be formed in how many ways?
  • A A) 15
  • B B) 20
  • C C) 30
  • D D) 40
Answer: Option B
Explanation: 6C3 = 20.
Q22
In how many ways can 3 boys be seated on 5 chairs?
  • A A) 10
  • B B) 30
  • C C) 60
  • D D) 120
Answer: Option C
Explanation: 5P3 = 5 × 4 × 3 = 60.
Q23
How many ways can the letters of the word "LEVEL" be arranged?
  • A A) 12
  • B B) 24
  • C C) 30
  • D D) 60
Answer: Option C
Explanation: 5! / (2! × 2!) = 30.
Q24
The number of ways to select 2 balls from 6 balls is—
  • A A) 12
  • B B) 15
  • C C) 18
  • D D) 20
Answer: Option B
Explanation: 6C2 = 15.
Q25
From 10 men, how many committees of 4 can be formed?
  • A A) 200
  • B B) 210
  • C C) 240
  • D D) 120
Answer: Option B
Explanation: 10C4 = 210.
Q26
How many 3-letter words can be formed from A, B, C, D with repetition allowed?
  • A A) 24
  • B B) 64
  • C C) 12
  • D D) 16
Answer: Option B
Explanation: 4³ = 64.
Q27
How many 4-digit numbers can be formed using digits 1 to 5 without repetition?
  • A A) 120
  • B B) 60
  • C C) 240
  • D D) 100
Answer: Option A
Explanation: 5P4 = 120.
Q28
In how many ways can you arrange the letters of the word "APPLE"?
  • A A) 60
  • B B) 120
  • C C) 240
  • D D) 360
Answer: Option A
Explanation: 5! / 2! = 60.
Q29
The number of combinations of 6 things taken 2 at a time is—
  • A A) 15
  • B B) 30
  • C C) 60
  • D D) 20
Answer: Option A
Explanation: 6C2 = 15.
Q30
In how many ways can 5 different pens be given to 3 students if each can get any number of pens?
  • A A) 15
  • B B) 125
  • C C) 243
  • D D) 3⁵
Answer: Option C
Explanation: Each pen → 3 choices ⇒ 3⁵ = 243.

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