1. The problem statement, all variables and given/known data From a group of 5 women and 7 men, how many different committees con- sisting of 2 women and 3 men can be formed? What if 2 of the men are feuding and refuse to serve on the committee together? Part 1: my attempt: for men, we have 7 choose 3 for woman, we have 5 choose 2. multiply together, and we get 350 possible committees Part 2 - what if 2 of the men are feuding. I'm trying to grasp the concept of that and what it means and how to build an equation for it. So we have 7 men and any 2 can be feuding, so if A and B are feuding, A can still serve with C, D, E, F, or G. So that means 5 ways for A. B can do the same, so 5 ways for B, 5 ways for C, 5 ways for D, 5 ways for E which is 30 ways. The men can be swapped around in 30 ways. Women can still be grouped in to 5 choose 2, so 30 x 10 = 300. I was able to work out the solution manually thinking it out, but I want to know how the author did it for part 2. author solution: There are C(5; 2)C(7; 3) = 350 possible committees consisting of 2 women and 3 men. Now, if we suppose that 2 men are feuding and refuse to serve together then the number of committees that do not include the two men is C(7; 3) - C(2; 2)C(5; 1) = 30 possible groups. Because there are still C(5; 2) = 10 possible ways to choose the 2 women, it follows that there are 30 10 = 300 possible committees what is C(2; 2) and C(5; 1)?? how did he come up with that?