3. The expression $\sum_{k=1}^{n}(-1)^{k} C_{n}^{k} C_{m, n-k}^{m}$ equals
A. 1
B. 0
C. 1 or 0
D. None of the above
3. $\mathrm{C}$ Hint: When $m=n$, the original expression is $1$; when $m<n$, the original expression is $0$. This can be examined by considering the coefficient of $x^{n}$ in $f(x)=(1-x)^{n} \frac{1}{(1-x)^{m+1}}=(1-x)^{n-m-1}$.