Three ways to count

Drag the temperature slider. On the hot end, the three curves lie right on top of each other — you'd think there was only one. Drag to the cold end and they peel apart into three completely different shapes. One is a fat spike at the lowest level and nothing anywhere else. Another holds flat across many levels and then falls off a cliff. The third is a smooth decay from the left edge downward.

These are three different rules about whether two particles can share a state: Bose-Einstein (the pile), Fermi-Dirac (the cliff), and Maxwell-Boltzmann (the smooth decay). Bosons can pile onto the same state without limit. Fermions can't share a state at all. Classical particles are indifferent — and once it's hot enough, the rule stops mattering.