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Wolfram Alpha defines multichoose as follows, "The number of multisets of length $k$ on $n$ symbols is sometimes termed $n$ multichoose $k$, denoted $\left(\binom{n}{k}\right)$ by analogy with the binomial coefficient $\binom{n}{k}$ $n$ multichoose $k$ is given by the simple formula  \left(\binom{n}{k}\right)=\binom{n+k-1}{k}=\left(n-1,k\right)!, $\left(\binom{n}{k}\right)=\binom{n+k-1}{k}=\left(n-1,k\right)!$,  where $(n-1,k)$ is a multinomial coefficient."