Combinatorics MOC
Binomial expansion
The binomial expansion states that num
where the so-called binomial coëfficients are given by
and is the number of ways to choose elements of a set of size .
See also Generalized binomial coëfficient.
Properties
-
\begin{align*}
{n \choose k} = {n \choose n-k}
\end{align*}
^P2
3. $$
\begin{align*}
{m+n\choose k} = \sum_{j=0}^k {m \choose j}{n \choose k-j}
\end{align*}
^P4
5. $$
\begin{align*}
\sum_{m=k}^n {m \choose k} = {n+1 \choose k+1}
\end{align*}