Question

A student dance committee is to be formed consisting of 2 boys and 3 girls. If the membership is to be chosen from 4 boys and 8 girls, how many different committees are possible?

Solution

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To know the number of different committees possible, given that we will choose 22 boys from 44 boys, and 33 girls from 88 girls, our equation will be

C(4,2)×C(8,3)=4!(42)!2!×8!(83)!3!C(4,2)\times C(8,3)=\dfrac{4!}{(4-2)!2!}\times\dfrac{8!}{(8-3)!3!}

since repetitions are not allowed and order does not matter in forming committees.

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