Question

The coach of a softball team has 8 good hitters and 9 poor hitters. He chooses 5 hitters at random.In how many ways can he choose 4 good hitters and 1 poor hitter?

Answer 1

He can choose 4 good hitters and 1 poor hitter in 630 different ways.

Explanation:

The order in which the hitters are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In how many ways can he choose 4 good hitters and 1 poor hitter?

4 good hitters from a set of 8.

1 poor hitter from a set of 9. So

`T = C_(8,4)*C_(9,1) = (8!)/(4!(8-4)!)*9 = 630`

He can choose 4 good hitters and 1 poor hitter in 630 different ways.