A student dance committee is to be formed consisting of 3 boys and 2 girls. If the membership is to be chosen from 8 boys and 7 girls, how many different committees are possible?

# A student dance committee is to be formed consisting of 3 boys and 2 girls. If the membership is to be chosen from 8 boys and 7 girls, how many different committees are possible?

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A student dance committee is to be formed consisting of 3 boys and 2 girls. If the membership is to be chosen from 8 boys and 7 girls, how many different committees are possible?

__ different committees are possible

A student
homework

S
9.9k points

In committees the order doesn't matter, i.e. AB is the same as BA. So we are dealing with combinations in this problem. We have to find the size of the committee formed by the boys and girls separately, and then multiply these together to find our answer.

For the boys:

$C(8,3) = 56$

and for the girls:

$C(7,2) = 21$

therefore,

$C(8,3) \cdot C(7,2) = 56 \cdot 21 = 1176$ committees are possible.

T
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