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## Homework Statement

Suppose that particles of two different species, A and B, can be chosen with

probability p_A and p_B, respectively.

What would be the probability p(N_A;N) that N_A out of N particles are of type A?

## The Attempt at a Solution

I figured this would correspond to a binomial distrib:

[tex]p_N(N_A) = \frac{N!}{N_A ! (N-N_A)!} p_A^{N_A} p_B^{N-N_A}[/tex]

Now I'm asked to consider the case where N gets large. Then I need to find [tex]p(N_A;N)[/tex] using 1) Stirling appox. and 2) the central limit theorem.

Not sure how to approach 1) since there are no log in my expression. Actually I don't quite get how to do 2) either. Any help would be much appreciated.