Okay, I am not sure if this is the right subforum, but here goes: An einstein solid is a solid composed of N quantum harmonic oscillators, which can store evenly spaced energy units q. Now suppose we have an einstein solid of N oscillators with q energy units, where q>>N. My book wants to derive an expression for the multiplicity of this solid, but I can't quite follow the approximations leading to the final expression: We have in general that that the multiplicity, Ω, of an einstein solid is given by the binomial: Ω = C(q+N-1,q) , where C() is the binomial coefficient. I wont verify this expression, because it is the approximations of it that bother me: In general we have from the definition of the binomial coefficient: Ω = C(q+N-1,q) = (q+N-1)!/((N-1)!*q!) My book approximates this to: Ω = (q+N)!/(q!*N!) with the argument that: "The ratio of N! to (N-1)! is only a large factor (N). I dont see what this has to do with the approximation. The multiplicity above gets far bigger with the approximation because it all depends on q. For instance, say q=100 and N=2. Then you get: Ωreal = 101!/100! = 101 Ωapprox = 102!/2! ≈ 50*Ωreal or i general for N=2: Ωapprox = q/2 * Ωapprox So in general how is this approximation valid? Am I plugging the numbers in the wrong way?