8. Simplify $\sum_{k=0}^{4} C_{n}^{k} C_{m}^{q-k}=$ $\qquad$ (Vandermonde's formula)
8. $\left(q_{m+n}\right.$ Consider $(1+x)^{n}$ and $(1+x)^{m}$ these two generating functions, on one hand $(1+x)^{n}(1+x)^{m}=(1+x)^{m+n}$ the coefficient of $x^{q}$ is $C_{m+n}$; on the other hand, the coefficient of $x^{q}$ is $\sum_{k=0}^{\eta} C_{n}^{k} C_{m}^{q-k}$.