Problem #55

Alice is having a party and has 20 guests, one of whom is her friend Bob. Bob starts a rumor about Alice. A person hearing this rumor for the first time will then tell the rumor to another person chosen uniformly and at random with the exception that no one will tell the rumor to Alice or to the person from whom they heard it. If a person who already knows the rumor (including Bob) hears it again, they will not tell it to anyone.

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