Question

An archaeology club has 25 members. How many different ways can the club select a president, vice president, treasurer, and secretary?There are different slates of candidates possible.(Simplify your answer.)

Answer 1

ANSWER

303,600 ways

EXPLANATION

We want to find a way of selecting four positions (president, vice president, treasurer and secretary) out of 25 members.

To do this, we apply permutation:

$P^{25}_4$

We have that:

$P^n_r=\frac{n!}{(n-r)!}$

Therefore, we have that:

$\begin{gathered} P^{25}_4=\frac{25!}{(25-4)!}=\frac{25!}{21!} \\ P^{25}_4=\frac{25\cdot24\cdot23\cdot22\cdot21!}{21!}=25\cdot24\cdot23\cdot22 \\ =\text{ }303600 \end{gathered}$

That is the number of ways they can be chosen.