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WAEC Further Mathematics 2006 Question 17

Question 17

Permutations and Combinations

A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?

  1. A.15
  2. B.40
  3. C.70
  4. D.175
Show the answer and explanation

Answer: D (175)

Explanation

Choose the chairman from the 5 men (5 ways), then the other 3 members from the remaining 7 people (⁷C₃ = 35 ways): 5 × 35 = 175.