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## Homework Statement

Explain why, for an ideal mixture, the mixing entropy is given by

ΔS

_{mixing}= k ln( Binomial Coefficient ( N, N

_{A})

where N is the total number of molecules and N

_{A}is the number of molecules of type A. Use Stirling's Approximation to show that this expression is the same as the result from the previous problem when both N and N

_{A}are large.

## Homework Equations

ΔS = Nk ln(V

_{f}/V

_{i})

Previous Solution: ΔS

_{mixing}= -Nk[ x ln (x) + (1-x) ln (1-x) ]

Stirling Approx: N! ≈ N

^{N}e

^{-N}√(2∏N)

## The Attempt at a Solution

I originally thought it might mean mathematically derive, but it looks like that is more related to the second part of the problem. I have no idea how to get from the equations they give me to the binomial coefficient part of the solution. I believe I can do the second part if someone can provide some assistance to the explanation.