Combinatorial estimate using Stirling's formula

Hey,

Could anyone please help with the following question?

"Estimate the number of decimal digits in nC(n/3) *as a function of n*, where n is divisible by 3"

Using Stirling's formula as n! ~ (sqrt[](2*pi*n))*((n/e)^n)*O(n) where O(n) is the error.

I substituted and cancelled the equation down to this:

nC(n/3) = n! / (2n/3)!(n/3)! = .... = (3^n)O(n) / (2^n)(sqrt[]pi*n)O(2n/3)O(n/3)

And this is irrational therefore I know I'm wrong but can't find my error.

Thanks a bunch!