一些组合公式

\(C_{n}^{m}=C_{n}^{n-m}\)
\(C_{n}^{m}=C_{n-1}^{m-1}+C_{n-1}^{m}\)
\(C_{n}^{n}+C_{n+1}^{n}+C_{n+2}^{n}+\ldots+C_{n+r}^{n}=C_{n+r+1}^{n+1}\)
\(C_{n}^{0}+C_{n}^{1}+C_{n}^{2}+\ldots+C_{n}^{n}=2^{n}\)
\(C_{n}^{0}+C_{n}^{2}+C_{n}^{4}+\ldots=C_{n}^{1}+C_{n}^{3}+C_{n}^{5}+\ldots=2^{n-1}\)
\(C_{n}^{m+1}=C_{n}^{m} \times \frac{n-m}{m+1}\)
\(C_{n}^{m}=\frac{n}{m} C_{n-1}^{m-1}\)
\(C_{n}^{k} C_{k}^{m}=C_{n}^{m} C_{n-m}^{k-m}\)
\(C_{n}^{0}+C_{n}^{2}+\cdots=C_{n}^{1}+C_{n}^{3}+\cdots=2^{n-1}\)
\(C_{m+n}^{r}=C_{m}^{0} C_{n}^{r}+C_{m}^{1} C_{n}^{r-1}+\cdots+C_{m}^{r} C_{n}^{0}\)\