### 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: This is a counting problem, so I need to think about how many choices I have at each stage of the selection process.
I have 15 players to choose from for the goalie position, so there are 15 ways to pick the goalie.
Once I have picked the goalie, I have 14 players left to choose from for the other six positions.
This is a combination problem, since the order of the six players doesn't matter.
I can use the formula for combinations, which is nCr = n!/(r!(n-r)!), where n is the total number of elements and r is the number of elements chosen.
In this case, n = 14 and r = 6, so the number of ways to choose the six players is 14C6 = 14!/(6!8!) = 3003.
To get the total number of ways to choose the starting team, I need to multiply the number of ways to choose the goalie by the number of ways to choose the other six players.
This is because for each possible choice of goalie, I have 3003 possible choices of the rest of the team.