Combinatorial estimate using Stirling's formula
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)(sqrtpi*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!