A typical stat mech. question is the following: If I have 5 bosons and energy E to divide among the bosons, what is the total number of possible configurations? I can't remember this answer, so if someone reading this can post it that would be appreciated. Now, I want to ask a slightly more difficult question. Suppose I have n bosons and I do not allow any boson to be excited past the kth energy level. How many possible configurations are there? Example: 2 bosons and I restricted to ground, first and second excited states. If we assume they bosons are indistinguishable, then there are 3^2 possible configurations: 00 01 02 10 11 12 20 21 22 Of course, the bosons are indistinguishable...so the possible configurations is reduced to six: 00 01 02 11 12 22 If there are 3 bosons restricted to the ground, first and second energy levels, then it turns out that there are 10 possible configurations. What is the general formula that counts the number of possible configurations for n bosons restricted to the kth excitation? I posted this same question in the probability forum....but I didn't refer to any physics....so one seemed to know (thus far anyway). I know that this is also a standard question...so the answer is definitely out there is well-known.