The binomial coefficient can be interpreted as the number of ways to choose k elements from an n-element set. How to write it in Latex ?

Definition

The binomial coefficient $\binom{n}{k}$ can be interpreted as the number of ways to choose k elements from an n-element set. In latex mode we must use \binom fonction as follows:

\frac{n!}{k!(n - k)!} = \binom{n}{k} = {}^{n}C_{k} = C_{n}^k
\[\frac{n!}{k!(n - k)!} = \binom{n}{k} = {}^{n}C_{k} = C_{n}^k\]

Properties

\frac{n!}{k!(n - k)!} = \binom{n}{k}
\[\frac{n!}{k!(n - k)!} = \binom{n}{k}\] 
\frac{A_n^k}{k!} = \binom{n}{k}
\[\frac{A_n^k}{k!} = \binom{n}{k}\]

where

A_n^k = \frac{n!}{(n-k)!}
\[A_n^k = \frac{n!}{(n-k)!}\]

are the different ordered arrangements of a k-element subset of an n-set

Pascal’s triangle

\binom{n}{k} =  \binom{n-1}{k-1} +\binom{n-1}{k}
\[\binom{n}{k} = \binom{n-1}{k-1} +\binom{n-1}{k}\]