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N Particles in a box

A box consists of a gas that we'll treat as distinguishable particles. The box is divided into equal parts (right-left), by a partition with a small hole in it. Assume the particles are non-interacting and move back and forth between the two sides through a hole in a statistically independent fashion.

a. if each distinguishable particle is considered to have two states, L and R, depending on its position in side L or side R, what is the total number of different states of all the particles considered together?

b. for a given number of total particles N (with half in the right side and half in the left side), what is the multiplicity of states possible in terms of N, N right, N left?

so for part a. I think that the total number of states is (2)^N because each event is an independent event (each particle)-- like tossing a coin?! There are too states that all of the particles are in one of the sides (one left +one right).

For the multiplicity I got g= N!/(2(N/2)!). Are my assumptions correct?

I dont know how to do the second part.

I'll appreciate any suggestions,

Thank you,

2. Relevant equations

3. The attempt at a solution

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# Homework Help: N Particles in a box

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