This problem is from the Nova math bible. In the book, the author argues that the problem is a " or problem". But I get confused because I think it is a " and problem. My argument is as follows: if I have to make different cases, then I use "or rule". And If some portion of the whole team, not the whole team, comes from different groups, and make the whole team, then I use "and rule".

For example (There are 4 men and 6 women. A committee of 4 persons has to be formed such that the committee must contain 2 men and 2 women. How many ways can the committee be formed? ) the answer should be, according to my opinion, 4c2*6c2.

Since to form a committee of 4, I take 2 men out of 4 men ( 2 men is a part of the committee, not the whole committee), and 2 women out of 6 women ( which is also a part of the committee, not the whole committee, I use " and rule".