I have N people and each of them has a uniform probability to belong to one of M countries. Now I wonder what is the distribution of the multiplicities?! I mean the number of countries with 1 person, 2 persons, 3 persons,... (no matter which country) Is there an equation for it? And what if the distribution is not uniform, but I know that some countries are more popular?! (a non-uniform distribution?) Is there a sensible measure of quantifying this redistribution of popularity? And does power law distribution play in at some point?