A club has 8 members. A President, a Secretary and a Treasurer are to be chosen from them, and no member can hold more than one post. In how many ways can the three posts be filled?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 336
The three posts are different, so it matters who gets which post: this is an arrangement (permutation). The posts are filled one by one and the choices are multiplied.
President: any of the 8 members, 8 choices
Secretary: any of the 7 members left, 7 choices
Treasurer: any of the 6 members left, 6 choices
Ways \(=8\times7\times6={}^8P_3=336\)
Why the other options are incorrect
Option (1) 56 — Incorrect. This is \(^8C_3\); it only picks 3 members and does not say who gets which post.
Option (2) 512 — Incorrect. This is \(8^3\), which lets one member hold two or three posts; the question does not allow that.
Option (3) 168 — Incorrect. This is only half of \(8\times7\times6\); every one of the 336 ways is a different result.