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Question

My soccer team has 16 players. I have to choose a starting lineup of a goalie and 10 regular players (the regular players are interchangeable). How many different starting lineups can I choose?

Accepted Answer

First we choose the goalie, and any of the 16 people can be the goalie. Then we choose 10 more players from the remaining 15 players, which is the same as choosing a committee. The answer is 161510=16155=1615 14 13 12 115 4 3 2 1=48,!048.