Geometry-Sequences with unlimited repeated values

  • Context: Undergrad 
  • Thread starter Thread starter thomasrules
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Discussion Overview

The discussion revolves around calculating the number of possible license plate combinations given specific constraints on symbols, particularly focusing on the inclusion of repeated symbols. The scope includes mathematical reasoning and combinatorial analysis.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant calculates the total combinations as 26^3 x 10^3 and proposes a method to find combinations with at least one repeated symbol using (26^3 - 25^3) x (10^3 - 9^3).
  • Another participant suggests considering the negation approach by calculating the number of plates with at most zero repeated symbols instead.
  • A third participant interprets "unlimited repeated values" to mean that any letter or digit can be used more than once, supporting the initial calculation as correct.
  • A practical note is raised regarding current license plate formats in New York, which differ from the problem's assumptions, including a different number of digits and specific exclusions of certain letters.

Areas of Agreement / Disagreement

Participants express differing views on the approach to calculating the number of plates, with no consensus reached on the best method. The practical considerations mentioned also highlight a divergence in assumptions about the problem's context.

Contextual Notes

Limitations include the assumption of the number of digits in license plates and the specific letters used, which may affect the calculations. The discussion does not resolve these contextual differences.

thomasrules
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Here is the question I cannot get it...

In a series of license plates, the first three symbols are any of the 26 letters in the alphabet and the last three are any of the 10 digits from 0 to 9.

How many plates can be formed in which at least one symbol is repeated?
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--------I know that 26^3x10^3 is the total possible combinations.
I thought that you would do this: (26^3-25^3)x(10^3-9^3)
 
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You want to know how many plates can be formed with at least one repeated symbol. Have you considered the negation? I.e. how many plates can be formed with at most zero repeated symbols?
 
I think the expression "unlimited repeated values" simply means that you can use any letter or digit more than once so your first expression would be correct.
 
Practical caveat. NY current plate has four digits (not three), but the first digit cannot be 0. In addition the letters I and O appear to have been omitted deliberately, looking too much like 1 and 0.
 

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