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1. I have a pile of n identical ping-pong balls and two boxes, labelled Box 1...

1. I have a pile of n identical ping-pong balls and two boxes, labelled Box 1 and Box 2. How many different ways are there to distribute the n balls into the two boxes? Explain why your answer is correct.

2. How many ways are there to distribute n ping-pong balls among k boxes?

3. I have n books with n different titles. I want to put them on shelves in my library. How many different ways are there to arrange them on one shelf? On two shelves? On k shelves?

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