Binomial coefficient

A binomial coefficient is the coefficient of the $x^k$ term in the polynomial expansion of the binomial power. These values are also present in the Pascal’s identity.

How do you calculate the binomial coefficient? ?

$${}_n{C}_r=\left(\begin{array}{c}n\\ r\end{array}\right)=\frac{n!}{k!(n-k)!}$$

An important property of binomial coefficients, given the symmetry in Pascal’s triangle is that: ?

$$\left(\begin{array}{c}n\\ k\end{array}\right)=\left(\begin{array}{c}n\\ n-k\end{array}\right)$$