Now that we know how to arrange balls into bins: let’s solve the original question: the number of ways a person can distribute 36 chocolates among five kids, and no one gets fewer than 5.
First, distribute five chocolates each to five kids so that everybody gets the minimum. That leaves 11, which may be distributed among five. The problem is identical to 11 indistinguishable balls into five separate bins or rearranging 11 similar balls + four similar partitions. That is given by:
15C4 = 1365
Note that it is identical to 15C11
