Is there any derivation for the problems:
$1.$Dividing $n$ identical things into $r$ identical groups where some groups may be empty or all $n$ things can go to any one group.
$2.$Dividing $n$ identical items into $r$ identical groups where there is at-least one item in every group.
I am not sure if this is modeled as some other known problem,what I am looking for, is a nice approach/derivation for solving these kind of models.