A total of balls, numbered 1 through are put into n urns, also numbered 1 through n

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A total of balls, numbered 1 through are put into n urns, also numbered 1 through n in such a way that ball i is equally likely to go into any of the urns 1, 2, ..., i. Find

a. The expected number of urns that are empty;

b. The probability that none of the urns is empty.

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