Configurational Entropy
There are counters, which are blue on one side and red on the other. If the macroscopic description of our state of interest is red on the checkerboard, how many corresponding micro-states are there?
A coin is tossed times, and it is noted that the number of heads is How many sequences of coin flips could have led to this result?
There are pigeon-holes for pigeons. If at most one pigeon can fit inside each hole, how many distinct arrangements are there for the pigeons to fit inside the holes?
Assume that we can distinguish each pigeon from the others.
There are six distinct boxes, each of which contains a single ball. If there are three red balls and three blue balls, how many distinct arrangements are possible?
There are pigeon-holes for 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 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.