# S5 permutation problem

11 football team members, including Dickson and Kingsley, are arranged in a row.

If Dickson cannot stand at the leftmost position and Kingsley cannot stand at the

rightmost position, how many possible arrangements are there?

### 1 Answer

- 知足常樂Lv 76 years agoFavorite Answer
Answer:

11! - 10! - 10! + 9! = 33022080

Explanation:

(1)

11! means the number of ALL arrangements in a row.

(2)

The first 10! means the number of arrangements by fixing Dickson to the leftmost position.

(3)

The second 10! means the number of arrangements by fixing Kingsley to the rightmost position.

(4)

9! represents the number of arrangements being double counted in (2) and (3). That is, fixing Dickson to the leftmost position and fixing Kingsley to the rightmost position.

2013-11-16 18:25:54 補充：

Helon, please read another method here: