Question
The number of ways to make 5 heaps of 3books each from 15 different books is


 ^{15}C_{3}
 ^{15}P_{5}
Hint:
Here we will be using the concept of arrangement of distinct objects into equal groups.
The correct answer is:
Detailed Solution :
5 heaps of 3 books each are to be made from 15 different books. We are to find in how many ways this can be done.
But this is applicable on if the groups are of unequal sizes.
In the given problem all the groups are of size 3, and there are 5 groups.
Hence,
Again, the equal groups will be arranged amongst themselves, which is possible in 5! ways. Thus, we can say that the required number of ways in which the 15 different books can be divided into 5 groups of size 3 is
In these type of questions, it is to be always remembered that separate approaches need to be adopted for distinct and identical objects. Here, the books were distinct or different.
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