Randomly sampling a “well-mixed” solution of Brownian particles

I place $N$ Brownian particles in $V$ liters of solution, shake until I assume that the particles are "well-mixed", and sample and randomly sample an $S$ liter volume. What is the probability distribution for the number of particles in my sample of $S$ liters?

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With homework like questions, you should include a discussion of your approach to the problem and where you are having difficulty. –  AdamRedwine Jul 31 '12 at 12:54
Even if the question was not assigned as homework, it is a homework style question. –  AdamRedwine Jul 31 '12 at 21:26
@AdamRedwine, alright, fair enough. –  S.G. Jul 31 '12 at 21:31