book shelf..........its all maths !!
Probability
Level
3
There are two works each of 3 volumes and two works each of two volumes. In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated.
The answer is 3456.
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1 solution
Lets label the books in accordance to its works. So we have AAA,BBB,CC and DD or total of10 books. AAA and BBB can be arranged 3! ways. CC and DD can be arranged 2! ways. Since we want the same works to be together, we can treat each work as 1 book. So, there essentially 4 'books' which can be arranged 4! So total of ways = 3! 3! 2! 2! 4!=3456 ways.