Fermions and Bosons in a distribution

[ZedCar]

Homework Statement

Consider a system of N distinguishable particles which are distributed across levels with energies 0, 1, 2, 3, 4, 5... The total energy of the system is U. Determine all the possible combinations of the particles in this system and hence determine the total number of microstates of the system.

N = 5
U = 3

The distributions are as follows:

state 0 1 2 3

4 0 0 1 Statistical weight=5, Fermions=0, Bosons=1
3 1 1 0 Statistical weight=20, Fermions=0, Bosons=1
2 3 0 0 Statistical weight=10, Fermions=0, Bosons=1

Homework Equations

The Attempt at a Solution

I understand the distributions and the statistical weight calculations.

Though how has it been determined that the Fermions in each distributions =0 and the Bosons=1 in each distribution?

Thank you!

 

[ZedCar]

If we consider another system.

N = 2
U = 8

The distributions are as follows:

state 0 1 2 3 5 6 7 8

100000001 Statistical weight = 2, Fermions = 1, Bosons = 1
010000010 Statistical weight = 2, Fermions = 1, Bosons = 1
001000100 Statistical weight = 2, Fermions = 1, Bosons = 1
000101000 Statistical weight = 2, Fermions = 1, Bosons = 1
000020000 Statistical weight = 1, Fermions = 0, Bosons = 1


Again I understand the configurations in the states 0 to 8, and also the statistical weights. Though again I am unsure as to how the numbers of Fermions and Bosons have been achieved.

 

[vela]

I think you must be leaving out some pertinent information.