1. The problem statement, all variables and given/known data If you have atoms that are normally located at the normal lattice positions or at an interstitial position where energy >ε, how can I find the probability that n interstitial positions are occupied by atoms? If we were to use large N how can I find the fraction of interstitial sites that are occupied as a function of the temperature? How do I find the microstate? 2. Relevant equations NCn n=E/ε 3. The attempt at a solution Assuming that there are N normal locations and N interstitial locations and the energy of an atom in a normal lattice position can be set to 0 I know that # of ways to arrange the intersticial atoms is N!/n!(N-n)! from there I don't know how to calculate de microstate nor the probability I attempted at a solution of random variables therefore P(n)=1/2n(N!/n!(N-n)!