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Ways of distributing money.

by toreil
Tags: distributing, money
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toreil
#1
Dec18-11, 06:23 AM
P: 6
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
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awkward
#2
Dec18-11, 01:20 PM
P: 327
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?
toreil
#3
Dec18-11, 01:49 PM
P: 6
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.

awkward
#4
Dec18-11, 07:00 PM
P: 327
Ways of distributing money.

To me, "We distribute a total of E dollars" sounds like the unit of distribution is a dollar. But other interpretations are certainly possible.
Ray Vickson
#5
Dec19-11, 02:15 PM
Sci Advisor
HW Helper
Thanks
P: 5,013
Quote Quote by toreil View Post
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.
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.

RGV


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