In how many ways can n - 5 + 1 balls, labelled from 5 to n be placed into 5 bags, labelled from 1 to 5?
(n > 4 and a bag may contain 0 balls.)
I hope you're kidding!
There are 5 choices for ball 1 (labeled 5), 5 choices for ball 2 (labeled 6), and so on. So the answer is $\displaystyle 5^{n-4}$.
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