### Instruction: Our water polo team has 15 members.  I want to choose a starting team consisting of 7 players, one of whom will be the goalie (the other six positions are interchangeable, so the order in which they are chosen doesn't matter).  In how many ways can I choose my starting team?### Response: To choose a starting team, I first need to choose a goalie and then choose six other players from the remaining 14.
For the goalie, I have 15 options, since any of the 15 members could play that position.
For each of those options, I then have to choose six players from the 14 who are not the goalie.
This is a combination problem, since the order of the six players doesn't matter.
The number of ways to choose 6 out of 14 is given by the binomial coefficient (14 choose 6), which is equal to 14! / (6! * 8!).
So for each of the 15 options for the goalie, I have (14 choose 6) options for the rest of the team.
To get the total number of ways to choose the starting team, I have to multiply these two numbers.
This gives me 15 * (14 choose 6) as the answer.