In how many ways can $4$ balls be placed in $8$ boxes if neither the balls nor the boxes are distinguishable?
Since all the boces are the same, this boils down to partitions of 4
4 in any one box
2 2 in any two boxes
1 3 in any two boxes
1 2 1 in any three boxes
1 1 1 1 in any four boxes
5 ways
+1752 
