I am trying to solve some problems based on this formula,but am facing some issues in determine whether or not consider ordering as important.
For Example:
In how many ways 15 different books can be divided five heaps of equal number of books ?
So here according to the answer the ordering of groups is not considered important,hence the answer given is $\frac {15!} {5!(3!)^5}$
and the same thing goes for this one :
In how many ways 3 piles can be formed out of 18 different books, which will be $\frac {18!} {3!(6!)^3}$
But for the following problem "There are three copies, each of four different books. In how many ways they can be arranged on a self ?"
This this is similar to divide 12 books into 4 sets of 3 books each, the answer given here considers the ordering important,why this change ?
Why in the first two the ordering not and on the third one it is important ? I guess (if the solution is correct) it is something related to copies but am not confident enough.
A good example of a problem where ordering should be considered important is say "In how many ways can 18 different books be divided equally among three students ?"
The solution should be $\frac {18!} {(6!)^3}$
But I am not much confident while in these problems so I will be grateful if somebody helps me to understand when to consider ordering important and when not to.