From a group of 4 men and 5 women, how many committees of size 3 are possible with 2 men and 1 woman, but 2 of the 4 men are feuding and refuse to serve on the committee together?
The answer I was given is to first calculate the total number of ways to select the men and women without restrictions, which is 4C2 * 5C1 = 30, and then subtract the ways to group those feuding men together, which is 2C2 * 5C1 = 5, giving the correct final answer as 25.
I don't understand why it is 2C2. Shouldn't it be 3C1? My reasoning behind this is that I group the pair of troublesome adults as one entity, so the 4 men "become" 3 units, and from there on, I choose 1 of the units.
Why is it 2C2?