(a) Give a generating function denoting the number of ways to select a subset from a set of three identical apples.

(b) Give a generating function denoting the number of ways to select a subset from a set of bananas. There are a total of four bananas, but they are bundled into two groups of two.

(c) Now pool the apples and bananas. Give the generating function for the number of ways to select a subset from the pooled set.

(d) How many ways are there to select three apples or bananas from the pooled set?

(e) Now suppose that you have 2 individual and identical oranges. Give a generating function for selecting from the oranges.

(f) Suppose you add the oranges to the set of apples and bananas. Give the generating function for the combined set.

(g) How many ways are there to select three pieces of fruit from the set of apples, bananas and oranges? (h) To verify your answer is correct, list the possibilities for selecting three pieces of fruit.