A committee of 7 people is to be formed form a group of 20 people, 11 of which are women?
a) In how many ways can this be done?
b)If the committee must consist of 4 women and 3 men, in how many ways can this be done?
The number of ways this can be done is $\displaystyle \binom{20}7=\frac{20!}{7!13!}$. We use combinations, for order doesn't matter here.
The number of ways this can be done is $\displaystyle \binom{11}4\binom93\binom{20}7$ (I believe...can someone verify this?)b)If the committee must consist of 4 women and 3 men, in how many ways can this be done?
Do you see why this is the case?
I hope this helps!
--Chris