# Combinatorics

posted by
**Layla**
.

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 different kinds of gas molecules (ni of each with

n1 + n2 + n3 = n). How does this affect the number of arrangements?