Basic Statistical Mechanics question

[ZedCar]

Homework Statement

An isolated system has N=3 distinguishable particles A, B, C with single particle states equally spaced at intervalsof E and a total energy U=3E.
ie the macrostate is defined by N=3, U=3E.

The system has single particle levels 0, E, 2E, 3E.

Homework Equations

The Attempt at a Solution

The beginning of the solution then begins with:

ni = {2, 0, 0, 1}
{1, 1, 1, 0}
{0, 3, 0, 0}

How were these sets of number obtained?

Thanks for any help!

 

[clamtrox]

These are the possible microstates. For {2, 0, 0, 1} , you have two particles with energy ε=0 and one particle with ε=3E, so Ʃε_i = 3E, as it should. For {1, 1, 1, 0}, one particle has ε=0, second has ε=E and third has ε=2E. For {0, 3, 0, 0} all particles have energy E. You should be able to convince yourself that these are the only possibilities to get total energy of 3E.