Suppose your vehicle is licensed in a state that issues...

Suppose your vehicle is licensed in a state that issues license plates that consist of three digits (between 0 and
9) followed by three letters (between $A$ and $Z$ ). If a license number is selected randomly, what is the probability that yours is the one selected?

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Key Concepts

Fundamental Counting Principle

This principle states that if there are several stages in an event and each stage has a certain number of independent choices, then the total number of outcomes is the product of the number of choices at each stage. It applies to many probability problems where outcomes are determined by sequential decisions.

Permutations with Repetition

When elements can be repeated in each position, the number of possible sequences or arrangements is computed by raising the number of available options to the power corresponding to the length of the sequence. This concept is key in counting problems where the same digit or letter can appear more than once.

Uniform Probability Distribution

In problems where every outcome in a finite sample space is equally likely, the probability of any single outcome is the reciprocal of the total number of outcomes. This fundamental concept is essential in determining probabilities for randomly selecting one element from a well-defined set of possibilities.

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