At an ambulance stations there are 5 nurses and 4 medics. Find in how many ways can we create a team with three people, where at least one of them is a medic.
I solved the problem this way: there are $4\cdot C_5^2$ ways to form a team with one medic and two nurses and $C_4^2 \cdot 5$ ways to form a team with two medics and one nurse and $C_4^3$ ways to form a team with tree medics.
So the answer will be $4\cdot C_5^2 + C_4^2 \cdot 5 + C_4^3 = 74$.
I am not sure if I am right with this answer, so this is the reason I am asking this question.