Combinatorics Harvard-MIT
2017


Problem - 4508

Kelvin and $15$ other frogs are in a meeting, for a total of $16$ frogs. During the meeting, each pair of distinct frogs becomes friends with probability $\frac{1}{2}$ . Kelvin thinks the situation after the meeting is cool if for each of the $16$ frogs, the number of friends they made during the meeting is a multiple of $4$. Find the probability of the situation being cool.


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