Question

A student was selected as a captain of a cooking team in a consumer and family studies class. The student could pick 2 of 5 girls and 3 of 7 boys to be on their team. What is the total number of different teams that this captain could select?

Answer 1

This captain could select 350 different teams.

Explanation:

The order in which the girls and the boys are picked is not important. For example, picking Daniela and Laura is the same as picking Laura and Daniela. So we use the combinations formula 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)!)`

Girls:

2 from a set of 5. So

`C_(5,2) = (5!)/(2!(5-2)!) = 10`

Boys:

3 from a set of 7. So

`C_(7,3) = (7!)/(3!(7-3)!) = 35`

Total:

`10*35 = 350`

This captain could select 350 different teams.