1. The problem statement, all variables and given/known data A certain club consists of 5 men and 6 women. a) How many ways are there to form a committee of 6 people if a certain pair of women refuse to serve on the same committee? b) How many ways are there to form a committee of 4 men and 3 women if two of the men refuse to serve on the same committee? 2. Relevant equations Permutations & Combinations P(n,k) = n(n - 1)(n - 2)...(n - k + 1) C(n,k) = P(n,k)/k! 3. The attempt at a solution a) Well, a pair = 2, so I intuitively want to exclude one of the women if she will not be in the committee when the other is in the committee. That gives 10 individuals (men and women). C(10,6) = 210 But this is not the answer in the book, unfortunately, so I know I'm not on the right track. b) C(6,3) = 20 would represent the combinations of the women's committee. For the men's 4 member committee, I feel like I want to exclude one of the 5 men because, like in the question above, there are two that cannot be in one committee together. That would leave 4 men to fill 4 spaces, so all the possible combinations are...1. C(6,3) x 1 = 20 But this too is very wrong according to the book. :-\ Can anyone help me to conceptualize this problem correctly? Thanks alot I really appreciate it!