If n balls are placed at random into n bins, what is the probability that exactly one bin remains empty? Show all your calculations. In particular, specify the sample space and the event you are interested in.
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Sample Space: We have n balls and n bins. Each ball can go into any of the n bins. So, there are n choices for each ball. Since there are n balls, the total number of ways to distribute the balls is $n^n$. Show more…
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