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Combinatorics

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Entropy
1. Suppose a room has n molecules of a gas. We divide the room into k equal
parts. How many ways can the molecules be split evenly between the parts (you
may assume that n is divisible by k)? How many ways can the molecules be in
only one part? What are the most common arrangements?
2. Suppose there are three diff erent kinds of gas molecules (ni of each with
n1 + n2 + n3 = n). How does this aff ect the number of arrangements?

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