From a group of 5 women and 7 men, how many different committees consisting 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?
For the second question the book says that there are 5 total invalid combinations, , but then provides no explanation as to how it arrived at that conclusion.
Could someone explain how this poorly executed textbook arrived at this conclusion for me?
I think you may be misunderstanding the book.
An "invalid" committee is one in which those two specific men serve together. Treat those two men as a single unit. There is one way, to choose that unit and ways to choose the third man. So there are to choose the men for an "invalid" committee. But there will still be ways to choose the women and so "invalid" committees.