[Math] Solving Large Factorial Division without writing out factorials

Question

I am calculating entropy for a physics problem and it requires solving this equation:

$\ Entropy = \frac{949!}{899! 50!} $

However, I am not sure how to solve this mathematically without reverting to writing out every single number on the top factorial until I reach 899. Is there a shortcut to solving factorial division without writing out these numbers?

Answer 1

You can use Stirling's approximation , in log form $\log n! \approx n(\log n-1)+\log\sqrt {2\pi n}$ to avoid overflow. It is quite accurate.