Problem 13

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

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