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OAU Post-UTME Mathematics 2022 (Batch A) Question 8

Question 8

Permutation and Combination

A committee of 5 members is to be formed from three females and four males. In how many ways can these be formed if at least one female is included as a member?

  1. A.12 ways
  2. B.21 ways
  3. C.24 ways
  4. D.72 ways
Show the answer and explanation

Answer: B (21 ways)

Explanation

There are 7 people, so 7C5 = 21 committees in all. An all-male committee of 5 is impossible (only 4 males), so all 21 include a female.