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

Step-by-step 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)=(15!)/((15-2)!)=(15\cdot14\cdot13!)/(13!)=210\text{ different ways to pick the 2 girls,} \\ P(19,2)=(19!)/((19-2)!)=(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*342=71820.`Answer

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