License Plates Officials from a particular state are...

Name: Problem 50, Chapter 8: Finite Mathematics and Calculus with Applications
Uploaded: 2020-05-14T02:28:23-08:00
Duration: 1 min 19 s
Channel: Foster Wisusik
Description: License Plates Officials from a particular state are considering a new type of license plate consisting of three letters followed by three numbers. If the letters cannot be repeated and must be in alphabetical order, calculate the number of possible distinct license plates.

License Plates Officials from a particular state are considering a new type of license plate consisting of three letters followed by three numbers. If the letters cannot be repeated and must be in alphabetical order, calculate the number of possible distinct license plates.

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Key Concepts

Combinations

This concept involves selecting a subset of items from a larger set where the order of selection does not matter. In problems like this, since the letters must be in alphabetical order and cannot be repeated, the selection of three letters from the alphabet is a combination problem rather than a permutation problem.

Multiplication Principle

This key concept in combinatorics states that if one event can occur in 'm' ways, and a second independent event can occur in 'n' ways, then the total number of ways both events can occur is m multiplied by n. Here, it is used to combine the number of ways to choose the letters with the number of ways to choose the numbers.

Alphabetical Order Constraint

The requirement that the letters be in alphabetical order limits the arrangements to only those selections that naturally follow the alphabet. This means that once three distinct letters are selected, there is exactly one acceptable ordering of them, simplifying the counting process.

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