2021 JMPSC Invitationals Problems/Problem 6

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 . If and are relatively prime positive integers, find .

Solution

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See also

1. Other 2021 JMPSC Invitationals Problems
2. 2021 JMPSC Invitationals Answer Key
3. All JMPSC Problems and Solutions

The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.