[QUOTE=Rafael;714765]The problem is attached as a PDF, pleas take a look./QUOTE]
First a comment in the form of a question. Why do you expect us to open another file? You could easily type the question yourself.
The question is: You have N bottles and n balls. You need to calculate the number of all possible distributions (configurations, states) of balls in the bottles considering that all balls and bottles are identical.
Now here is another critical comment: the formula in that post has nothing to do with the solution of the problem as it is stated. Because the bottles are identical as are the balls this is simply a question of how one partitions the integer n into N or fewer summands.
Here is an example: .
We could have: that is four ways.
Now there is no neat closed solution to this question. All solutions to the integer partition problem are recursively defined sequences (functions).
Here are some examples: if then , while then .
Now I actually question the use of the word identical in the original question. The suggested answer implies otherwise.