How Many Ways to Distribute 10 Units of Energy Among 5 Bosons?

[StephenSmith]

Homework Statement

In a system with equidistant energy levels how many ways can you distribute 10 units of energy among 5 bosons? The energy of the ground state(i=0) is 0, and the energy levels are at equal distances from each other.

Homework Equations

The Attempt at a Solution

 

[CompuChip]

That depends on whether you need to need to distribute exactly 10 or at most 10. Let's assume that it's exactly, i.e. E = 10 has been given.

Maybe it's useful starting with a simpler example with 3 units of energy. You can give them all to one boson, i.e. (3, 0, 0). Or you can give them to another boson: (0, 3, 0) or (0, 0, 3). Question for you: are these the same situation or can you tell the bosons apart?

Then there is of course (2, 1, 0). What other possibilities can you see? (No complex math here, you can just draw them out on a piece of paper).