Question

The newly elected president needs to decide the remaining 8 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

Answer:

The members of the cabinet can be appointed in 121,080,960 different ways.

Step-by-step explanation:

The rank is important(matters), which means that the order in which the candidates are chosen is important. That is, if we exchange the position of two candidates, it is a new outcome. So we use the permutations formula to solve this quesiton.

Permutations formula:

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

$P_{(n,x)} = \frac{n!}{(n-x)!}$

If there are 14 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?

Permutations of 8 from a set of 14. So

$P_{(14,8)} = \frac{14!}{(14-8)!} = 121,080,960$

The members of the cabinet can be appointed in 121,080,960 different ways.