Am I doing this right?

Question

Ok if I have 6 men, 7 women and I want to make a committee of 4 of them, and I want the number of ways I can have a committee with both sexes. OK the way I think I can do it is by doing
nPr(4,2)*nCr(7,2) for the number of ways i can order 2 women chosen from 7 in a possible of 2 positions.
Now I do the same for the number of men.
Next I do nPr(4,3) *nCr(7,3) for the combinations of 3 women chosen to fill 3 positions. Do the same for the men.
Now I add these two parts together. Is this a valid way of doing this type of problem?

Answer 1

committee of 1women and 3 men + 2 women and 2 men + 3 women and 1 men

nCr(7,1)*nCr(6,3)+
nCr(7,2)*nCr(6,2)+
nCr(7,3)*nCr(6,1)

Answer 2

For the number of committees of 4 using men and women you can have 3 men and 1 woman, 3 women and 1 man, 2 men and 2 women.

C(6,3)*C(7,1)+C(7,3)*C(6,1)+C(6,2)*C(7,2)

Answer 3

There are the following configurations of the committee:
(1) MMMF
(2) MMFF
(3) MFFF
Config 1 is 6C3 *7
Config 2 is 6C2 * 7C2
Config 3 is 6*7C3
Add them up for the answer.