in Combinatory
162 views
0 votes
0 votes
How many ways are there to pack nine identical DVDs into three indistinguishable boxes so that each box contains at least two DVDs?
in Combinatory
162 views

1 Answer

0 votes
0 votes

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.

Related questions