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Homework Help: Ways of distributing money.

  1. Dec 18, 2011 #1
    I am studying for a statistical physics exam and have been struggling with the statistic parts, especially calculating the number of microstates. I am starting to understand most questions but have no clue how to handle this one.

    1. The problem statement, all variables and given/known data

    We distribute a total of E dollars among a population of N people. The rules are that each person can get a max of 1 dollar and that E < N, find the number of ways this can be done.

    2. Relevant equations


    3. The attempt at a solution

    W = [itex]\frac{\left(E\times100\right)!}{100!\left(\left(E-1\right)\times100\right)!}\times p_{e}[/itex] where [itex]p_{e} = \frac{E}{N}[/itex] the average value received by each person
    Last edited: Dec 18, 2011
  2. jcsd
  3. Dec 18, 2011 #2
    OK, so each person either does or does not get a dollar, and there are E dollars total.

    Hmmm... so isn't this exactly the same as selecting a subset of size E from the N people?
  4. Dec 18, 2011 #3
    As far as I'm aware because the question states that each person gets a maximum of 1 dollar the actual amount of money each person receives is counted in cents rather than dollars.
  5. Dec 18, 2011 #4
    To me, "We distribute a total of E dollars" sounds like the unit of distribution is a dollar. But other interpretations are certainly possible.
  6. Dec 19, 2011 #5

    Ray Vickson

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    Homework Helper

    This would correspond to an unphysical situation in which Money is neither Bose-Einstein (person can have any number of dollars) or Fermi-Dirac (person can have either 1 dollar or none). Of course, money IS unphysical, so maybe the 100 cents interpretation is OK.

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