I'm trying to reproduce Excel's COMBIN function in C#. The number of combinations is as follows, where number = n and number_chosen = k:
$${n \choose k} = \frac{n!}{k! (n-k)!}.$$
I can't use this formula because the factorial overflows the computer's capacity really quick. Int32 can only do up to 12!, Int64 up to 20!, and double up to a whopping 170! after that I'm on my own.
How can I get the same results with a formula more gentle to the computer?