# How to use Sterling's approximation with calculator

1. Oct 17, 2014

### leroyjenkens

1. The problem statement, all variables and given/known data
w!/(w-n)! = number of ways of distributing n* distinguishable particles in w distinguishable states

w = number of distinguishable states
n = number of indistinguishable particles

How many ways are there to put 2 particles in 100 boxes, with no particles sharing a box.

2. Relevant equations
ln(n!) = nln(n) - n

3. The attempt at a solution

I get ln(n!) = 100ln(100) - 100 = 360.5 and
ln(98!) = 98ln(98) - 98 = 351.3

I need to raise both of those numbers to e to get the final answer, but my calculator can't do that. The final answer is a relatively small answer that a calculator can handle, but getting to that answer is impossible unless you do some intermediate step. That step involves doing something with these numbers before I raise them to e. I can't figure out what that step is. Thanks.

2. Oct 17, 2014

### Orodruin

Staff Emeritus
Well, you don't really need to compute the factorials to compute 100!/98!. Have you been told explicitly to use Stirling's formula?