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this is the IOIB (identical Objects, Identical Boxes) problem. According to the problem, each box has at least two DVDs.

Let each box be labelled, B1, B2, B3.


∴  We need to find the number of partitions of 9 into 3 parts where $B_{i}$ $\geqslant $ 2

There are 3 ways


9 = 2+2+5

9 = 2+3+4

9 = 3+3+3

(NOTE: since all the objects and boxes are same, all other permutations of the partitions will be same)

Thus, there are 3 ways to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs.

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admin asked May 1, 2020
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How many different terms are there in the expansion of $(x_{1} + x_{2} +\dots + x_{m})^{n}$ after all terms with identical sets of exponents are added?