Question

A committee of five members is to be randomly selectedfrom a group of nine freshman and seven sophomores.Which expression represents the number of different committeesof three freshman and two sophomores that can be chosen?

Answer 1

The answer would be the product of the number of 3 freshman groups by 2 sophomores groups.

The number of 3 freshman groups is given by

`C^9_3=(9*8*7)/(3*2*1)=84`

The number of 2 sophomore groups is given by

`C^7_2=(7*6)/(2*1)=21`

Now, doing their product

`21*84=1764`

We have 1764 different committees of three freshman and two sophomores.