# Thread: Discrete Mathamatics

1. ## Discrete Mathamatics

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?

2. Originally Posted by msmall13@yahoo.com
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?
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.

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 $\displaystyle \binom{11}4\binom93\binom{20}7$ (I believe...can someone verify this?)

Do you see why this is the case?

I hope this helps!

--Chris

3. Hello,
Originally Posted by Chris L T521
The number of ways this can be done is $\displaystyle \binom{11}4\binom93{\color{red}\binom{20}7}$ (I believe...can someone verify this?)

Do you see why this is the case?

I hope this helps!

--Chris
Why is there the red part ?