GULF 2015 Problem 3

We have a large supply of black, white, red and green hats. And we want to give $8$ of these hats to $8$ students that are sitting around a round table. Find the number of ways of doing that in each of these cases (assuming for the purposes of this problem that students will notchange their places, and that hats of the same color are identical) a) Each hat to be used must be either red or green. b) Exactly two hats of each color are to be used c) Exactly two hats of each color are to be used, and every two hats of the same color are to be given to two adjacent students. d) Exactly two hats of each color are to be used, and no two hats of the same color are to be given to two adjacent students. e) There are no restrictions on the number of hats of each color that are to be used, but no two hats of the same color are to be given to two adjacent students.