200概率困难derivationlong

Full Distribution of Empty Urns via Stirling Numbers

题目

Six distinguishable balls are thrown independently and uniformly at random into 5 distinguishable urns. Let $E$ denote the number of empty urns. Derive the probability mass function $P(E = k)$ for every possible value of $k$ , expressing each probability as an exact fraction.

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你的答案

P(E=0)

P(E=1)

P(E=2)

P(E=3)

P(E=4)