good chemistry is complicated, and a little bit messy LW 

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Ok, it's been communicated that using the entropy function would provide a better approximation to nCr. So here is such a formula:
Let H(eps) := eps.log_2(eps)(1eps)log_2(1eps) be a binary entropy function. Then binom(n, eps.n) is approximately equal to 2^(n.H(eps)). Where eps is short for epsilon. Update: Note that this uses the more common Stirling formula which is slightly less accurate as it truncates terms in the series (instead of approximating them like the formula i posted before). In reply to Re(2): Pascal triange...
by gumby

