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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?

A committee of five members is to be randomly selectedfrom a group of nine freshman and seven sophomoresWhich expression represents the number of different comm class=

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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

[tex]C^9_3=\frac{9\times8\times7}{3\times2\times1}=84[/tex]

The number of 2 sophomore groups is given by

[tex]C^7_2=\frac{7\times6}{2\times1}=21[/tex]

Now, doing their product

[tex]21\times84=1764[/tex]

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

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