Not sure about this answer.
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
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)