Find the value of $$\binom{n}{0}-\binom{n}{1}+\binom{n}{2}-\binom{n}{3}+\cdots +(-1)^n\binom{n}{n}$$
The answer is $\boxed{0}$. This can be shown by setting $x=-1$ in the binomial expansion $$(1+x)^n=\binom{n}{0} +\binom{n}{1} x + \cdots + \binom{n}{n}x^n$$