Permutation and Combination Questions and Answers

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Q41
How many ways can 6 people be arranged around a circular table?
  • A A) 720
  • B B) 120
  • C C) 60
  • D D) 120
Answer: Option D
Explanation: (n – 1)! = 5! = 120.
Q42
In how many ways can 4 different medals be awarded among 10 students?
  • A A) 210
  • B B) 5040
  • C C) 504
  • D D) 720
Answer: Option B
Explanation: 10P4 = 5040.
Q43
How many words can be formed from "BANANA"?
  • A A) 60
  • B B) 120
  • C C) 720
  • D D) 360
Answer: Option A
Explanation: 6! / (3! × 2!) = 60.
Q44
The number of ways to select 1 or more balls from 3 balls is—
  • A A) 6
  • B B) 7
  • C C) 8
  • D D) 3
Answer: Option B
Explanation: 2³ − 1 = 7.
Q45
How many ways can a president, secretary, and treasurer be chosen from 6 persons?
  • A A) 120
  • B B) 60
  • C C) 90
  • D D) 20
Answer: Option A
Explanation: 6P3 = 120.
Q46
From 5 boys and 3 girls, a group of 4 must be chosen. How many ways?
  • A A) 35
  • B B) 70
  • C C) 100
  • D D) 105
Answer: Option B
Explanation: 8C4 = 70.
Q47
How many 2-digit numbers can be formed using digits 1, 2, 3, 4 without repetition?
  • A A) 6
  • B B) 8
  • C C) 12
  • D D) 16
Answer: Option C
Explanation: 4P2 = 12.
Q48
How many ways can 10 students stand in a line if two insist on standing together?
  • A A) 9! × 2
  • B B) 10!
  • C C) 9!
  • D D) 8! × 2
Answer: Option A
Explanation: Treat them as one block. Total = 9! × 2.
Q49
In how many ways can 2 men and 2 women sit in a line such that men sit together?
  • A A) 24
  • B B) 12
  • C C) 48
  • D D) 36
Answer: Option B
Explanation: Treat men as one unit. Total = 3! × 2! = 12.
Q50
The number of ways to arrange letters of "MADAM" is—
  • A A) 60
  • B B) 120
  • C C) 30
  • D D) 20
Answer: Option C
Explanation: 5! / (2! × 2!) = 30.

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