Distribution of n identical object in r different boxes if empty boxes are not allowed

Distribution of n identical object in r different boxes if empty boxes are allowed

Distribution of n distinct object in r different boxes (empty box allowed)

Distribution of n distinct object in r different boxes (empty box not allowed)

Distribution of n distinct objects into r distinct boxes if in each box at least one box is placed

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

Find the number of distributions of 5 distinguishable balls in 3 identical cells,an empty cell allowed.