### Instruction: 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?### Response: I need to choose 11 players out of 15, and then choose two captains out of those 11.
To choose 11 players out of 15, I can use the combination formula: 15 choose 11, which is 15! / (11! * 4!) = 1365.
To choose two captains out of 11, I can use the combination formula again: 11 choose 2, which is 11! / (9! * 2!) = 55.