Number of spanning trees containing a given forest

We consider all spanning trees of a complete simple graph $\mathrm{\Gamma }$ on $n$ vertices that contain a given $m-$forest $F$. We show that the number of such spanning trees, $\tau (F)$, doesn’t depend on the structure of $F$ and is completely determined by the number of vertices $q_i(i=1,\mathrm{.}\mathrm{.}\mathrm{.},m)$ in each connected component of $F$. Specifically, $\tau (F)=q_1{q}_2\cdots q_m{n}^{m-2}$.