\begin{equation*} (1 + 1)^n = {n \choose 0}1^n + {n \choose 1}1^{n-1}1 + {n \choose 2}1^{n-2}1^2 + \cdots + {n \choose n-1}1\cdot 1^{n-1} + {n \choose n}1^n\text{.} \end{equation*}