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Assume that Nicole has 25 apples that she puts, one by one, into k different buckets....

Assume that Nicole has 25 apples that she puts, one by one, into k different buckets. Each apple has an equal probability 1/k of landing in any of the buckets. Compute the probability that at least two apples end up in the same bucket for the following values of 1) k = 30 and 2) k = 25.

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