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ISI2026-MCS-PCA | Question: 27

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Every person is given a random color independently and uniformly from the set $\left\{C_{1}, \ldots, C_{k}\right\}$. What is the expected number of different colors that a household with $k$ members have received?

  1. $k\left(1-\left(1-\dfrac{1}{k}\right)^{k}\right)$
  2. $k\left(1-\dfrac{1}{k}\right)^{k}$
  3. $k\left(1-\dfrac{k!}{k^{k}}\right)$
  4. $1$

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