Problem – 13
How many ways are there to distribute seven indistinguishable balls into seven distinguishable bins?
Solution :
Distributing k indistinguishable balls into n distinguishable boxes, without exclusion, corresponds to forming a combination of size k with unrestricted repetitions, taken from a set of size n. Therefore, there are C(n+k-1, k) different ways to k distribute k indistinguishable balls into n distinguishable boxes, without exclusion.
Using the above theorem total number of ways = C(7+7-1,7) = C(13,7) = 1716