in Combinatory
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How many ways are there to pack eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD?
in Combinatory
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this is the IOIB (identical Objects, Identical Boxes) problem. According to the problem, each box has at least one DVD.

Let each box be labelled, B1, B2, B3, B4. B5.


$\therefore$  We need to find the number of partitions of 8 into 5 parts where $B_{i}$ $\geqslant $ 1

There are 3 ways


8 = 1+1+1+1+4 

8 = 1+1+2+2+2

8 = 1+1+1+2+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 eight identical DVDs into five indistinguishable boxes so that each box contains at least one DVD.

edited by

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