A basketball team has 9 players, in how many different ways can the coach select 2 players to be the captains for tonight's game.

Since the order doesn't matter 36 is the answer

Since order does not matter, you use the "n choose k" formula for unique combinations ...

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

In this case n=9 and k=2 so

c=9! / (2!*7!)

c=36

There are 36 unique ways to pick 2 captains from 9 players.