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Fruit Counting with Balls and Sticks

Here is a question that may puzzle you initially. But it has a fairly simple solution. Consider you have 3 kinds of fruits Apples, Bananas, and Coconuts. Assume that you have an unlimited source. Then how many ways are there to pick 4 fruits? There are 15 for this case.

4A,4B,4C
3A1B,3A1C,3B1A,3B1C,3C1A,3C1B
2A1B1C,2B1A1C,2C1A1B
2A2B,2B2C,2A2C

Now think about another puzzle. How [...]