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

303,600 ways

Step-by-step 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=(n!)/((n-r)!)`

Therefore, we have that:

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

That is the number of ways they can be chosen.