Question

In how many different ways can a ski club consisting of 20 people select a person for its officers? the positions available are president, vice president, treasurer, and secretary. no person can hold more than one positions and the each office is filled in order.

Answer 1

There are 116,280 ways to select the officers.

Since order is important, we use permutations:

$P(20,4)=\frac{20!}{(20-4)!}=\frac{20!}{16!}=116280$