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=(n!)/((n-r)!)`

In this case we have:

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

Therefore there are 2184 ways to choose the officers.