1. A commitee of seven is to be selected from 10 teachers and 12 students. How many different committees are possible if there is to be a majority of students with at least one teacher on the committee?

2. Sarah, Vanessa, jessica, David, Paul and Mark are seated at a round table. How many different arrangements are possible if the boys and girls must alternate and Jessica can not sit beside Paul.

Ah, permutations and combinations - my worst weakness. Could someone please explain to me how to do these sort of questions?