### 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: First let's count the number of ways we can choose the goalie.
There are 15 choices for the goalie.
Now let's count the number of ways we can choose the other six players.
I think we can use the binomial coefficient, $\binom{n}{k}$, which counts the number of ways of choosing $k$ items from a set of $n$ items.
Right. In this case $n=14$ and $k=6$.
So there are $\binom{14}{6} = 3003$ ways of choosing the other six players.