Stirling's Approximation

Stirling's Approximation is needed to solve for the entropy of mixing. Your calculator can't solve N! if N is greater than 69.

 1! = 1          =  1

 2! = 1*2        =  2

 3! = 1*2*3      =  6
   
 4! = 1*2*3*4    = 24

... and so on to ...

68! ...        = 2.48 * 10^+96

69! ...        = 1.71 * 10^+98

70! ...        = overflow error on calculator