I am supposed to show that N!/(N-n)! = N^n where 1<<n<<N I used stirling's approximation to show that N! = e^(NlnN-N) and (N-n)! = e^[(N-n)ln(N-n) - N + n]. I took the ratio of these two terms to get e^[NlnN-N-(N-n)ln(N-n) + N - n]. I cancelled terms and get N!/(N-n)! = N^N/[(N-n)^(N-n)e^n], which isn't N^n. btw, stirlings says that lnN! = NlnN - N. Can someone give me a hint? That would be great.