Maxwell-Boltzmann vs Bose-Einstein vs Fermi-Diract statisics

A good conceptual starting point is to like the example that is mentioned at The Harvest of a Century by Siegmund Brandt (2008).

Consider a system with 2 particles and 3 states. Remember that:

in quantum statistics (Bose-Einstein statistics and Fermi-Dirac statistics), particles are indistinguishable, therefore, we might was well call both of them A, as opposed to A and B from non-quantum statistics
in Bose-Einstein statistics, two particles may occupy the same state. In Fermi-Dirac statistics

Therefore, all the possible way to put those two particles in three states are for:

Maxwell-Boltzmann distribution: both A and B can go anywhere:
State 1 State 2 State 3
AB
AB
AB
A B
B A
A B
B A
A B
B A
Bose-Einstein statistics: because A and B are indistinguishable, there is now only 1 possibility for the states where A and B would be in different states.
State 1 State 2 State 3
AA
AA
AA
A A
A A
A A
Fermi-Dirac statistics: now states with two particles in the same state are not possible anymore:
State 1 State 2 State 3
A A
A A
A A

TODO: show on forumulas. TODO experimental data showing this. Please.....

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