+1348 In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty?
+6 Let the boxes be B1 and B2.
It it obvious, that under given condition, EITHER box B1 OR box B2 must be empty.
If box B1 is empty, then all 8 indistinguishable balls are in box B2: so, there is only one such distribution.
If box B2 is empty, then all 8 indistinguishable balls are in box B1: so, there is only one such distribution.
In all, there are 1 + 1 = 2 such distinguishable distributions.
