Question

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.

Answer 1

Since the order doesn't matter 36 is the answer

Answer 2

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.