jmc

Question

I coach a soccer team with 15 members. I want to choose a starting lineup consisting of 11 players, two of whom will represent the team in the captains meeting at the beginning of the game. In how many ways can I choose my starting lineup, including designating the two captains?

Accepted Answer

There are 152=105 ways to select the 2 captains from among the 15 players on the team. We then need to choose the remaining 9 starters from among the remaining 13 players, which can be done in 139=715 ways. This gives us a total of 152139=105715=75,!075 ways.