Question

he newly elected president needs to decide the remaining 3 spots available in the cabinet he/she is appointing. If there are 14 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed

Answer 1

The members of the cabinet can be appointed in 2184 ways.

Explanation:

The rank matters, which means that we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

How many different ways can the members of the cabinet be appointed

3 spots from a set of 14 candidates. So

`P_((14,3)) = (14!)/((14-3)!) = 2184`

The members of the cabinet can be appointed in 2184 ways.