Question: a. Find the generating function for number of ways to buy r T-shirts, if there are 4 colors (red, blue, black, white) of T-shirts available,

a. Find the generating function for number of ways to buy r T-shirts, if there are 4 colors (red, blue, black, white) of T-shirts available, where at most 3 blue T-shirts, and at least 2 T-shirts of each color red, white, and black is allowed.

b. Use part (a) to find the number of ways to buy 12 T-shirts with the above conditions.

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