A society has 9 members. A President, a Vice-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 four posts be filled?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3024
The posts are different, so order matters: the posts are filled one after another, with one person fewer each time.
President: 9 choices; Vice-President: 8; Secretary: 7; Treasurer: 6
Ways \(=9\times8\times7\times6=\,^9P_4=3024\)
Why the other options are incorrect
Option (2) 126 — Incorrect. This is \(^9C_4\), which only chooses 4 people and does not say who holds which post.
Option (3) 6561 — Incorrect. This is \(9^4\), which lets one member hold more than one post.
Option (4) 504 — Incorrect. This is \(9\times8\times7\), which fills only 3 posts.