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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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    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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