# Show that? #(P(N', n))/(P(N,n)) ~~ ((N')/N)^n# #(N', N, n) in ZZ^+# #(N', N )">>" n# #P(x,y) = (x!)/((x-y)!)# Stirling Approx allowed

##### 1 Answer

Jul 18, 2018

Stirling's approximation says that

In this way, we can approximate

Since the second condition says that

And since all of these we know that

Returning to the original question,

completing the derivation.