Partitioning Generating Functions

[Shoney45]

Homework Statement

Finda generating function for the number of ways to distribute r identical objects into 3 indistinguishable boxes.

Homework Equations

The Attempt at a Solution

It is the problem of "indistinguishable boxes" that has me flummoxed. I know that if the boxes were distinct, then my generating function would be:

(1 + x + x^2 + x^3 +...)^3

But I am not sure what to do with the matter of "indistinguishable boxes".

 

[Shoney45]

The only thing I can come up with is that order doesn't matter in terms of what goes into the boxes. In other words, if I am partitioning the integer 5 into 2,2,1...and I put each of those integers into one each of my three boxes...then 2,2,1 is the same as 1,2,2.

I still can't figure out though how that pans out as an expression in a generating function.

 

[Shoney45]

We just hit up our professor, and he said the question is misplaced in the book. He said we don't have enough material yet to solve this question. So forget about this question.