WAEC Further Mathematics 2025 Paper

Concept:Since the chairman is a specific post that must be held by a man, first select the chairman from the men, then choose the remaining ordinary members from the remaining people.Explanation:There are $5$ men and $3$ women, giving a total of $8$ people.First choose the chairman from the $5$ men: $^5 C_1 = 5$ ways.Now the chairman is already one member, so the remaining $3$ committee members must be chosen from the other $7$ people.Number of ways to select these $3$ members is $^7 C_3$.$$^7 C_3 = \frac{7!}{3!4!} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35$$Therefore, total number of committees is:$$5 \times 35 = 175$$So the chairman's post is treated as distinct, and not simply as "at least one man" on the committee.Answer:$175$ ways, which is option B.