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## Homework Statement

"Consider the case of 10 oscillators and eight quanta of energy. Determine the dominant configuration of energy for this system by identifying energy configurations and calculating the corresponding weights. What is the probability of observing the dominant configuration?"

## Homework Equations

The Weight (W): W = N!/[(N

_{0}!)(N

_{1}!)(N

_{2}!)(N....!)]

## The Attempt at a Solution

I know that the answer is 10!/[(1!)(1!)(3!)(5!)] = 5040 for the dominant weight, but when I used (instead of 3! & 5!, I used) 10!/[(4!)(4!)] which equals 6300. Why is 3! & 5! the dominant energy configuration used then? I assume you can't use two of the same N (populations/states)? Is that right?

I also got the answer to the rest of the question too [W

_{TOTAL}=20170, & Probability = W/Wtotal = 5040/20170 = 0.25], but I couldn't get passed the very first part of figuring out the dominant energy configurations for this system.

-Thanks

***NOTE: The text that I'm given is Physical Chemistry 9th Ed. by Atkins. I know that the question is from some Statistical Thermodynamics and Kinetics book by Engel & Reid. If it matters.. I feel like the book I have is a little difficult to follow