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I'm stuck on this problem:

Consider eight particles, four black and four white. Four particles can fit right and four can fit left of a permeable membrane. Assuming that each arrangement is equally likely due to random motion of the particles, how many different arrangements are there?

So for instance BBBB|WWWW and WWWB|BBBW are possible arrangements.

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    Do BBBW|WWWB and BBWB|WWWB count as the same arrangement?2012-12-21
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    Hint: Once you determine which particles are on the left side of the membrane, you already know which are on the right side. So how many possible combinations of particles are there on the left side?2012-12-21
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    Yes, I think BBBW|WWWB and BBWB|WWWB count as the same arrangement since particles in a compartment don't have a natural ordering in any way.2012-12-21
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    I also thought of the left implies right idea. So, is the answer then just $\binom{8}{4}$? Since you have to choose any 4 out of the 8 particles which settles the entire distribution?2012-12-21
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    Are the particles distinguishable? If not, then there are just $5$ arrangements: any number of black particles from $0$ to $4$ can be on the left.2012-12-21

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