Problem 1. From a group of 8 women and 6 men a committee consisting of 3 men and 3 women is to be formed. How many different committees are possible if
(a) 2 of the men refuse to serve together;
(b) 1 man and 1 woman refuse to serve together?

Problem 2. In how many ways can you write abstemious in such a way that the vowels follow their natural order a, e, i, o, u. For example, you are allowed to write basesimout but not besasimout.

Problem 3. In how many ways can a dozen books be placed on four distinguishable shelves
(a) if the books are indistinguishable copies of the same title?
(b) if no two books are the same, and the positions of the books on the shelves matter?