Classical Mechanics
# Configurational Entropy

$8$ red on the $4\times 4$ checkerboard, how many corresponding micro-states are there?

There are counters, which are blue on one side and red on the other. If the macroscopic description of our state of interest isThere are $15$ pigeon-holes for $2$ pigeons. If at most one pigeon can fit inside each hole, how many distinct arrangements are there for the $2$ pigeons to fit inside the $15$ holes?

Assume that we can distinguish each pigeon from the others.

There are $5$ pigeon-holes for $5$ pigeons. Three of the pigeons are white, and the other two are grey. If each hole can hold at most a single pigeon, how many micro-states are there for the $5$ pigeons to fit into the 5 hole?

Assume that we can distinguish each pigeon by their color, but cannot distinguish two pigeons of the same color.