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2021 JMPSC Invitationals Problems/Problem 6

Revision as of 15:04, 11 July 2021 by Samrocksnature (talk | contribs) (Created page with "==Problem== Five friends decide to meet together for a party. However, they did not plan the party well, and at noon, every friend leaves their own house and travels to one of...")
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Problem

Five friends decide to meet together for a party. However, they did not plan the party well, and at noon, every friend leaves their own house and travels to one of the other four friends' houses, chosen uniformly at random. The probability that every friend sees another friend in the house they chose can be expressed in the form $\frac{m}{n}$. If $m$ and $n$ are relatively prime positive integers, find $m+n$.

Solution

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