A choir has 3 spots open for altos, and 8 altos are interested in them. In how many ways can the open spots be filled?

Multiply the spots, by the number of people willing to take them: so, 8*3 = 24. There are 24 different ways in which the alto positions can be taken.

Since order is not important for unique combinations, we need to apply the "n choose k" formula ...

n! / (k! (n-k) !), n=number of elements to choose from, k=number of choices made

In this case:

8! / (3! (8-3) !)

56

So there are 56 unique threesomes possible with 8 members.