Question

A club needs to choose 3 members to be president, vice president and treasurer. If there are 15people in the club, how many ways can they assign the three rolls?

Answer 1

Given:

Total people in the club = 15

Number of choices = 3

Let's find the number of ways they can assign the three rolls.

To find the number of ways, apply the permutation formula since there can be replacement in this situation.

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

Where:

n = 15

r = 3

Thus, we have:

$\begin{gathered} ^{15}P_3=\frac{15!}{(15-3)!} \\ \\ =\frac{15!}{12!} \\ \\ =\frac{15*14*13*12!}{12!} \\ \\ =15*14*13 \\ \\ =2730 \end{gathered}$

Therefore, there are 2730 ways they can assign the three roles.

ANSWER:

b. 2730