Consider a model Thermodynamic assembly in which the allowed(nondegenerate) stat

Question

Consider a model Thermodynamic assembly in which the allowed(nondegenerate) states have energies 0, , 2,3. The assembly has four distinguishable (localized)particles and a total energy U=6. a) Tabulate the nine possible distributions of the fourparticles among the energy levels n, where n = 0, 1,...
I have manage to find 5 agreeing with the initial constraintsof N=4 and U=6. But it seems there are 9. Cansomeone please help. text: Classical and Statistical Thermodynamics byAshley Carter. Problem 12-6
a) Tabulate the nine possible distributions of the fourparticles among the energy levels n, where n = 0, 1,...
I have manage to find 5 agreeing with the initial constraintsof N=4 and U=6. But it seems there are 9. Cansomeone please help. text: Classical and Statistical Thermodynamics byAshley Carter. Problem 12-6

Explanation / Answer

Let the distinguishable particles be named A,B,C,D. Since the four states are non-degenerate, each has to have oneparticle each. So, the possibilities are :     3-1, 2-1, -1,0-1         A      B      C    D        A      B      D   C        A      C      B   D   ............................and so on. The total possibilities are : 4! = 24.

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