Question

The bowling team at Lincoln High School must choose a president, vice president;and secretary. If the team has 14 members, how many ways could the officers bechosen?

Answer 1

We have 14 members and we need to arrange them in three positions, then we need to use a permutation.

A permutation is given as:

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

In this case we have:

$\begin{gathered} _{14}P_3=\frac{14!}{(14-3)!} \\ =\frac{14!}{11!} \\ =\frac{14\cdot13\cdot12\cdot11!}{11!} \\ =14\cdot13\cdot12 \\ =2184 \end{gathered}$

Therefore there are 2184 ways to choose the officers.