“Stuffing some stuff into buckets” How many ways are there to sort n distinct objects to r buckets?
\begin{equation} r^{n} \end{equation}
grouping with entirely indistinct objects You can simply reframe the grouping problem as permutation of the objects with r-1 dividers along with your old n objects. i.e.: sort this thing — So:
\begin{equation} \frac{(n+r-1)!}{n! (r-1)!} \end{equation}