# Weird games

Author: aruzhan
Problem has been solved: 20 times

Русский язык | English Language

6 children play handshakes. Initially, each of them has two free hands. Each turn, each of them randomly selects 2 of all free hands and joins them with a handshake (possibly a handshake between two hands of the same person). Ultimately, all 12 hands are shaking other hands. The expected value of the number of closed chains of children can be represented as an irreducible fraction $\frac{m}{n}$, for positive integers $m$ and $n$. Find $m+n$.