Question

I need help on figuring out if the situation involves a permutation or a combination. I also need help on determining the number on possible arrangements.

Answer 1

Explanation

Since each member of the committee has a distinct responsibility, this means that the order of selection matters. A different order means that two people would have different responsibilities. So we conclude that we must compute the possible arrangements using permutation.

We have:

$\begin{gathered} P(15,2)=\frac{15!}{(15-2)!}=\frac{15\cdot14\cdot13!}{13!}=210\text{ different ways to pick the 2 girls,} \\ P(19,2)=\frac{19!}{(19-2)!}=\frac{19\cdot18\cdot17!}{17!}=342\text{ different ways to pick the 2 boys.} \end{gathered}$

Multiplying these results, we get the total number of ways to form the committee:

$210\times342=71820.$Answer

To compute the number of possible arrangements we use permutation, and there are 71820 ways to form the committee.