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*}

Proof.

in-context