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We are playing a game of blindfolded musical chairs with 20 blindfolded people and 40 chairs....

  1. We are playing a game of blindfolded musical chairs with 20 blindfolded people and 40 chairs. When the music stops each person picks a chair uniformly at random and sits on it.

I. What is the probability that some chair has at least two people sitting on it?

II. What is the probability that some chair has at least three people sitting on it?

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