5.2 The Pigeonhole Principle pg.354

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SUMMARY

The discussion centers on the application of the Pigeonhole Principle to demonstrate that among 100,000,000 wage earners in the United States earning less than $1,000,000, at least two individuals must have earned the same amount last year. Given that there are only 1,000,000 possible income values (from $0 to $999,999), the principle asserts that with more wage earners than income values, duplication is inevitable. This conclusion is reached without the need for complex equations, relying solely on logical reasoning.

PREREQUISITES
  • Understanding of the Pigeonhole Principle
  • Basic knowledge of income ranges and distributions
  • Familiarity with logical reasoning techniques
  • Awareness of statistical concepts related to population and sample sizes
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  • Research the implications of the Pigeonhole Principle in probability theory
  • Explore examples of the Pigeonhole Principle in real-world applications
  • Study basic statistical distributions and their properties
  • Learn about combinatorial mathematics and its relevance to counting problems
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Students in mathematics, educators teaching probability and statistics, and anyone interested in logical reasoning and combinatorial principles.

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Show that if there are 100,000,000 wage earners in the United States who earn less than 1000,000 dollars, then there are two who earned exactly the same amount of money, to the penny, last year.

There are no equations.


Please solve the question. I really need this question. Thanks
 
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You need to show your ideas, so we can work together and get the solution, so let's start with the basics:

If this is true, why would it be true? How many possible incomes are possible?
 

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