Question: Ten empty buckets are lined up in a row. Each bucket is labelled. A set of n balls are randomly thrown one after the other

Ten empty buckets are lined up in a row. Each bucket is labelled. A set of n balls are randomly thrown one after the other into the buckets. What is the expected number of throws that are necessary until two buckets have at least one ball in them? For example, if the first ball landed in bucket 1, and the second ball landed in bucket 2, then it only took me 2 throws. If the first ball landed in bucket 1 and the second ball landed in bucket 1, and the third ball landed in bucket 4, then it took me 3 throws. After all n balls are thrown, what is the probability that the total number of balls in bucket 1 and bucket 2 is 4? (Not 4 balls in each. A total of 4 balls in bucket 1 and bucket 2)

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