Question

On a skiing trip there are five people but only three pairs of skis how many different groups of three could ski

Answer 1

10 different groups can ski.

This is a combination of 5 items taken 3 at a time:
$_5C_3=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{120}{12}=10$