Theorem 3.4.2. Combinations of a subset with replacement.
The number of ways to select an unordered group of r items from a set of n distinct items is
\begin{equation*}
_{n+r-1}C_r = {{n+r-1} \choose r} = \frac{(r+n-1)!}{r!(n-1)!}
\end{equation*}