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WAEC Further Mathematics 2025 Question 40

Question 40

Permutations and Combinations

A medical group consists of 7 general practitioners and 5 surgeons. In how many ways can an outreach team of 5 medical personnel be selected if the team must have at least three general practitioners?

  1. A.175
  2. B.350
  3. C.525
  4. D.546
Show the answer and explanation

Answer: D (546)

Explanation

3 GPs: ⁷C₃ × ⁵C₂ = 350; 4 GPs: ⁷C₄ × ⁵C₁ = 175; 5 GPs: ⁷C₅ = 21. Total 546.