Question

The coach has 4 positions to fill on her softball team. There are 11 girls who are interested in being on the team. How many combinations of the four positions can she choose for her team?

Answer 1

Since the coach has 4 positions to fill on her softball team. There are 11 girls who are interested in being on the team.

We have to the number of combinations of the four positions can she choose for her team.

A formula for the number of possible combinations of r objects from a set of n objects is given by:

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

`^1^1(C_(4))= (11!)/(4!(11-4)!)`

=
`= (11!)/(4!(7)!)`

=
`=(11 * 10 * 9 * 8 * 7!)/(4 * 3 * 2 * 7!)`

`=(11 * 10 * 9 * 8)/(4 * 3 * 2)`

= 330

So, 330 combinations of the four positions she can choose for her team.