Permutation and Combination - Selections with Restrictions

Doris, a matchmaker, is to organize a dinner for \(4\) men and \(4\) women.

1. How many ways can she select these \(8\) people from a list of \(10\) men and \(10\) women?
2. Before the dinner, the \(8\) people were introduced to each other. What is the total number of handshakes if each person, excluding Doris, shakes hands just once with everyone else?
3. After the dinner, Doris decides to split them up into groups. However, one of the \(4\) men had to leave straight after dinner. How many ways can Doris split the remaining \(7\) people into \(3\) groups if each group is to consist of at least one man and at least one woman?