committee. Complete parts $($a$)$ through $($c$)$ below.

a$.$ How many different ways can the four officers be appointed?

There are $,$ different ways to appoint the four officers.

b$.$ How many different ways can a committee of five be appointed?

There are $\_\_\_\_$different ways to appoint a committee of five.

c$.$ What is the probability of randomly selecting the committee members and getting the five youngest of the qualified candidates?

$P($getting the five youngest of the qualified candidates$)=$

$($Type an integer or a simplified fraction.$)$