Ways of distributing money.

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Y3JpcHRpb24gSW4gc3VtbWFyaXplZCBmb3IgRSBkb2xsYXJzIGFtIGFubm91bmNlIGFtb3VudCBhZGRyZXNzLCBhbmQgaGF2ZSBiZWVuIHJ1bGxpbmcgd2l0aCB0aGUgbnVtYmVyIG9mIDEgZG9sbGFyIn summary, the problem states that a total of E dollars is distributed among N people, with each person receiving a maximum of 1 dollar. The task is to find the number of ways this can be
  • #1
toreil
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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.

Homework Statement



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.

Homework Equations



?

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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  • #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?
 
  • #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.
 
  • #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.
 
  • #5
toreil said:
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
 

1. How do different economic systems distribute money?

There are several different economic systems that distribute money in different ways. In capitalist systems, money is primarily distributed through market forces, where individuals and businesses make choices about how to spend and invest their money. In socialist systems, the government plays a larger role in distributing money through taxes and social programs. In mixed economies, there is a combination of both market forces and government intervention.

2. What are some potential consequences of unequal distribution of money?

Unequal distribution of money can lead to a variety of consequences. Some potential negative effects include poverty and income inequality, which can lead to social unrest and political instability. It can also limit economic growth and hinder overall societal progress.

3. How does inflation impact the distribution of money?

Inflation can impact the distribution of money in several ways. When the cost of goods and services increases, those with fixed incomes or lower wages may struggle to afford basic necessities. Inflation can also widen the wealth gap, as those with more assets and investments may see their value increase while those without may struggle to keep up with rising prices.

4. Are there any ethical considerations when distributing money?

Yes, there are ethical considerations when it comes to distributing money. Some people believe that everyone should have equal access to resources and opportunities, while others argue that individuals should be able to keep the money they earn through their own efforts. Additionally, there may be ethical concerns about how money is earned and whether it is distributed in a fair and just manner.

5. How do government policies and regulations affect the distribution of money?

Government policies and regulations can have a significant impact on the distribution of money. For example, tax policies can influence how much money individuals and businesses have to spend or invest. Welfare programs and social safety nets can also impact the distribution of money, as they provide financial support to those who may otherwise struggle to meet their basic needs. Additionally, regulations on businesses and industries can affect the distribution of profits and wages among different groups of people.

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