Heather just had new neighbours move in next door and would like to make a fruit basket for
them. When her husband returned from the grocery store he had a bag containing apples,
bananas, and oranges. How many different possibilities are there for a fruit basket consisting
of exactly 36 pieces of fruit if
(a) there is an ample supply of apples and bananas, but there are only 4 oranges?
(b) there are 16 of each kind of fruit?
(c) there is an ample supply of bananas and oranges, and there are 4 distinguishable apples
(one Fuji, one Macintosh, one Spartan, and one Ambrosia)?
(In each case, fruit baskets are distinguished
solely by how many of each type of fruit they contain.)