For this question, we must prove whether this statement is true or false.
The number of open paths of length $2$ in $K_m,_n$ is ($1/2$) $mn(m + n − 2)$
I know that when there is a graph $K_m,_n$, it has $m!n!/2(m-n-1)!$ open paths. But I do not know how to apply this formula to when we only want to know how many open paths of length $2$ there are.
Hint:
To have an open path of length two in $K_{m, n}$, either we have to select two distinct vertices from $m$ vertices and $1$ vertex from $n$ vertices OR select two distinct vertices from $n$ vertices and $1$ vertex from $m$ vertices.