# Thread: select a committie with brother and sister

1. ## select a committie with brother and sister

Hi,

A sub committee of 3 women and 2 men is to be chosen at random from a committee of 5 women and 7 men. In the original committee are a brother and sister. Find the probability that both the brother and sister are both selected to work on the sub committee

cheers

2. Originally Posted by Joel
Hi,

A sub committee of 3 women and 2 men is to be chosen at random from a committee of 5 women and 7 men. In the original committee are a brother and sister. Find the probability that both the brother and sister are both selected to work on the sub committee

cheers
I would say that for the numerator you would have C(5,1)*C(7,1) for the selection of the brother and sister.

For the denominator the total possibilities would be C(5,3)*C(7,2).

Result: .167

3. Originally Posted by mikeyS
I would say that for the numerator you would have C(5,1)*C(7,1) for the selection of the brother and sister.
For the denominator the total possibilities would be C(5,3)*C(7,2).
You have the denominator correct, but not the numerator.
Try $\binom{4}{2}\binom{6}{1}$. WHY?

4. Originally Posted by Plato
You have the denominator correct, but not the numerator.
Try $\binom{4}{2}\binom{6}{1}$. WHY?

I guess I tried this one before my second cup o' joe.

Looking at the sub-committee we will have groups like:
sister, not sister, not sister and brother, not brother

So we place the sister and brother leaving 4 and 6 members left to fill 2 and 1 spot(s), respectively. Thus to fill the remainder we have C(4,2) and C(6,1)