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Homework Help: Stirling's formula probability

  1. Jan 22, 2009 #1
    Use Stirling's formula, n!=sqrt(2 pi n) n^n e^{-n}, to estimate the probability that all 50 states are represneted in a group of 50 councilmen chosen at random.

    I think it should be:

    [tex]P=\frac{50!}{50^{50}} [/tex]

    So using Stirling's formula, we get:

    [tex]P=\frac{\sqrt{2 \pi 50} 50^{50} e^{-50}}{50^{50}}[/tex]
    [tex]P=\sqrt{2 \pi 50} e^{-50}[/tex]

    is this the correct approach?
     
  2. jcsd
  3. Jan 23, 2009 #2
    Re: probability

    Presuming each councilman represents one of the 50 states, your work is correct!
     
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