Originally Posted by

**hyperchondriac** Hi everyone, as you can see this is my first post. I should start by saying that my stats is so rusty that I'm not even sure if this is a basic or advanced problem! Anyway, here goes:

I have a very large sample (~30,000,000) of particles of a known size distribution (split into 5 fractions) from which I want to pick a smaller sample (~30,000), and determine the probability of getting various different size distributions. If the original sample of *M *particles consists of *A, B, C, D *and *E *particles in each size fraction, and I am picking *m* particles, the probability of picking *a, b, c, d *and *e* particles is:

$\displaystyle \frac{^AC_a \times ^BC_b \times ^CC_c \times ^DC_d \times ^EC_e} { ^MC_m}$

First of all, I hope that this is correct! As I said, my stats is very rusty. The problem with this is that, for example, *B* is 850,000 and *b* is 850, which is beyond the realms of Excel's calculations. Even worse, *B*<*C*<*D*<*E*!

So, my question is: is there an approximate method I could use in this case that would avoid these enormous numbers?

I hope I have explained my problem properly! Thank you in advance for any help you can give.