Thermodynamic assembly - Statistical Thermodynamics

[PePaPu]

Homework Statement

Consider a model thermodynamic assembly in which the allowed (nondegenerate) states have energies 0, ε, 2ε, 3ε.The assembly has four distinguishable (localized) particles and a total energy U = 6ε. Tabulate the nine possible distributions of the four particles among the energy levels nε where n = 0, 1...

Homework Equations

The Attempt at a Solution

I have tried tabulating it but I can only find five possible distributions that add up to 6ε.

3ε...2...1...1...
2ε.....1.....2...3
ε...1...3...2...
0...2...1......1

I'm stumped as to where to go form now and I cannot find the other four. Is there some part of the theory I'm getting wrong or I'm not understanding?

 

[Charles Link]

It looks correct to me. The other possibility is if you consider the particles distinguishable, then you need to label the particle at a given energy level. If that is the case, and I counted correctly, I get 44 different states.