Question

From the 12 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, power forward, small forward, shooting guard and point guard. However, there are only three of the 12 players who can play center. Otherwise, there are no restrictions. How many ways are there for her to select the starting line-up?

Answer 1

990

Explanation:

The center position can be selected in 3 different ways, the other 4 players can be selected in combinations of 11 players (the center is already selected) taken 4 at a time.

By the Fundamental Principle of Counting, there are

`3\displaystyle\binom{11}{4}=3*\displaystyle(11!)/(4!(11-4)!)=3*\displaystyle(11!)/(4!7!)=990`

ways for her to select the starting line-up.