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How to use Sterling's approximation with calculator

  1. Oct 17, 2014 #1
    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. jcsd
  3. Oct 17, 2014 #2


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