This can be solved using permutations.You can get more into this online or just accept a quick answer here.
Since there are certain roles to be filled this is a permutation.
You need a somewhat smart calculator for this.
If I remember this right you'd type in the number of people you are choosing from, P , and then the places you are trying to fill.
So it should look like this:
13 P 5
You can find where permutations and combinations are in your calculator using a handbook or the internet but usually it looks like nPr for permutation or nCr for combination.
