SOLUTION: A committee has seven men and four women. If four people are selected to go to a​ conference, what is the chance that the group is two men and two​ women?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A committee has seven men and four women. If four people are selected to go to a​ conference, what is the chance that the group is two men and two​ women?       Log On


   

Question 1058221: A committee has seven men and four women.
If four people are selected to go to a​ conference, what is the chance that the group is two men and two​ women?

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
There are 11C4 ways to go or 330 ways.
There are 7C2 ways to choose the men (21)
There are 4C2 ways to choose the women (6)
They are independent, meaning the choice of men does not affect the choice of the women.
That product is 126
The probability is 126/330, or 21/55
The other choices should add up to 204
one man, 3 women is 7*4=28
no men, 4 women is 1 way
3 men, 1 woman is 35*4=140 ways
4 men, 0 woman is 35 ways
They add up to 204.