$$ \begin{align}& \binom{n}{k_1,k_2,\dots,k_m}\\&=\frac{n!}{k_1!k_2!\cdots k_m!}\\&=\binom{k_1}{k_1} \binom{k_1+k_2}{k_2}\cdots \binom {k_1+k_2+\cdots+k_{m}}{k_{m}}\end{align} $$
Is there a combinatorial interpretation of this formula? I found this answer which I think is for interpreting it as picking from a set of indistinguishable objects (and is hence cumulatively taking away from an initial set of $n$ objects), but what about for assigning n distinct objects into $m$ "boxes"?
