Combination problem, what's wrong with my reasoning?

[fishingspree2]

Form a team by choosing 4 persons among 4 women and 7 men. You need at least 2 women in the team. How many ways to do it?

My solution:
1. Choose 2 women among the 4 availaible women. There is 2C4 ways of doing it.
and
2. Choose 2 persons among the 9 remaining people, there is 2C9 of doing it.

2C4 * 2C9 = 216 ways.

This is wrong, but I can't see why...

 

[tiny-tim]

hi fishingspree2!

This is wrong, but I can't see why...

because you're counting some teams more than once

eg if the team contains exactly 3 women, A B and C, then you're counting that team 3 times:

once for A and B being chosen first, once for B and C, and once for C and A