Making groups of 2., probability of getting a certain group? Let us say we have $n$ people $p_1, ...., p_n$ where $n$ is even. We find some random way to make groups of 2, and we are interested in if $p_i$ gets in a group with $p_j$, if $p_i$ gets $p_k$, $p_j$ gets in a group with $p_k$, and etc. Let us say that we have $m$ 'groups' that we wonder whether they occur. How can we calculate this probability? For example, what's the probability that a group is $(p_1,p_2)$ OR $(p_2,p_3)$?

There are $n-1$ equally likely ways to choose $p_2$'s partner. Of these, $2$ are "favourable."
