Permutation and Combination Questions and Answers

Practice Mode
Showing 10 of 64 questions
Q51
How many ways can 8 identical pens be distributed among 3 students?
  • A A) 36
  • B B) 45
  • C C) 120
  • D D) 15
Answer: Option B
Explanation: Stars and Bars formula: (n + r - 1)C(r) = (8 + 3 - 1)C(8) = 10C8 = 45.
Q52
How many ways can 5 cards be drawn from 52?
  • A A) 52C5
  • B B) 52P5
  • C C) 5C52
  • D D) 26C2
Answer: Option A
Explanation: Combination (order doesn't matter): 52C5.
Q53
The number of ways to arrange 7 persons in a round table is—
  • A A) 720
  • B B) 120
  • C C) 720/7
  • D D) 6!
Answer: Option D
Explanation: Circular permutation: (7-1)! = 6!.
Q54
How many different committees of 3 can be formed from 5 men and 4 women if at least one woman is included?
  • A A) 56
  • B B) 84
  • C C) 64
  • D D) 72
Answer: Option B
Explanation: Total – all men = 9C3 – 5C3 = 84 - 10 = 74.
Q55
In how many ways can digits 1, 2, 3, 4, 5 be arranged so that even digits occupy even positions?
  • A A) 12
  • B B) 24
  • C C) 48
  • D D) 60
Answer: Option A
Explanation: Position constraint. Total = 2! × 3! = 12.
Q56
The number of ways of selecting a president and vice-president from 8 candidates is—
  • A A) 56
  • B B) 64
  • C C) 72
  • D D) 56
Answer: Option A
Explanation: 8P2 = 56.
Q57
How many 5-letter words can be made from "EXAM"?
  • A A) 120
  • B B) 60
  • C C) 24
  • D D) 0
Answer: Option D
Explanation: Only 4 letters available; can't form 5-letter word.
Q58
How many ways can you arrange the letters of "ASSASSIN"?
  • A A) 2520
  • B B) 10080
  • C C) 3360
  • D D) 420
Answer: Option C
Explanation: 8! / (4! × 2! × 1! × 1!) = 3360.
Q59
From digits 1–9, how many 4-digit even numbers can be formed if repetition is not allowed?
  • A A) 1680
  • B B) 3024
  • C C) 2880
  • D D) 504
Answer: Option C
Explanation: Last digit even. Total = 4 × 8 × 7 × 6 = 1344.
Q60
How many words can be formed from "COMMITTEE"?
  • A A) 50400
  • B B) 45360
  • C C) 90720
  • D D) 7560
Answer: Option B
Explanation: 9! / (2! × 2! × 2!) = 45360.
Questions and Answers for Competitive Exams Various Entrance Test