How many teams can be made from 11 people? The question asks this:
Five places exist on a team. $11$ total people. $6$ come from district A, $4$ from district B and $1$ from district C.
How many different groups of five are there?
How many different groups of five are there if each team must contain at least one person from each district?
Question 1 is easy, it is simply $\binom{11}5$, but I do not know how to do the second question.
Thanks

The player from C must always be on the team. We have $\binom{10}{4}$ possibilities how to choose the rest of the players. There are $\binom{6}{4}$ of them that would not contain a player from B and $\binom{4}{4}$ that would not contain a player from A. So the result is 
$\binom{10}{4} - \binom{6}{4} - \binom{4}{4}.$
