Maximizing the number of states In statistical mechanics, why do we maximize the number of states? i.e. why do we maximize
$$
\frac{N!}{n_1!n_2!...}
$$ 
where $N$ is total number of particles and $n_i$ is the number of particles in the $i$'th state. 
 A: The Fundamental Postulate of Statistical Mechanics says that 

For an isolated system with an exactly known energy and exactly known composition, the system can be found with equal probability in any microstate consistent with that knowledge. 

The isolated system with an exactly known energy and composition is what @Marius means by "the microcanonical ensemble". Therefore, in this system, any microstate (ie any one particular distribution of particles in the set of states) is equally likely. 
Now because the probability of finding the system in a particular distribution (ie a macrostate) is given by the number of microstates giving rise to the macrostate divided by the total number of microstates available, we can find the most likely macrostate by maximising the expression you have (which is what we call the equilibrium state). 
In fact, when the total number of particles in this system becomes very large, you can show that it is exponentially unlikely to find the system away from the equilibrium state. 
