 More compactly, 
Then, by expanding formula_94 in powers of formula_95, one can check that the probability formula_96 of finding exactly formula_97 clusters which each has formula_98 particles is
The number density formula_100 of formula_98-clusters can therefore be calculated as
This is also called the "cluster size distribution".The grand potential formula_103 is equal to formula_104, which, using the thermodynamic relationship formula_105, leads to the following expansion for the pressure