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.