Question

math The newly elected president needs to decide the remaining 3 spots available in the cabinet he/she is appointing. If there are 15 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed

Answer 1

2730 ways

Explanation:

Given that,

There are 15 eligible candidates for these positions.

The newly elected president needs to decide the remaining 3 spots available in the cabinet he/she is appointing.

It is a concept based on permutations.

`P(n,r)=(n!)/((n-r)!)`

Put n = 15 and r = 3

`P(15,3)=(15!)/((15-3)!)\\\\=(15!)/(12!)\\\\=(15* 14* 13* 12!)/(12!)\\\\=15* 14* 13\\\\=2730`

Hence, 2730 ways can the members of the cabinet be appointed