For \(n \in \mathbb{N}\text{,}\)
\(\displaystyle \binom{n}{0} = 1\)
\(\displaystyle \binom{n}{n} = 1\)
\(\displaystyle \binom{n}{1} = n\)
\(\displaystyle \binom{n}{n-1} = n\)
\(\displaystyle \binom{n}{r} = \binom{n}{n-r}\)
\(\displaystyle \binom{n+1}{r+1} = \binom{n}{r} + \binom{n}{r+1}\)