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

Distribution of n identical object in r different boxes if empty boxes are not 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 12 identical balls in 5 different boxes so that none of the box is empty is

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

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

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