You live in a state where the car license plates have three...

You live in a state where the car license plates have three letters (without duplications on a plate) on the left followed by three numbers (again without duplications) on the right. The letters are randomly selected from the 26 letters of the alphabet, and the numbers are randomly selected from the ten integers 0 to 9. Assuming that all plates are available, and that you are assigned a plate randomly, what is the probability that you will get a plate that reads: ABC012?

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Key Concepts

Uniform Probability Distribution

A uniform probability distribution occurs when all outcomes in the sample space are equally likely. This concept is important because, under the assumption that every license plate is available and assigned randomly, each plate, including the specific one in question, has an equal chance of being selected.

Permutations

Permutations refer to the arrangement of elements in a specific order, often without repetition. This concept is essential when determining the total number of possible arrangements of letters or numbers from a set, especially when order matters.

Multiplication Principle

The multiplication principle states that if one event can occur in a number of ways and a second independent event can occur in another number of ways, then the total number of ways both events can occur is the product of the two counts. This principle is used to calculate the total number of outcomes for the license plate by multiplying the number of ways to arrange letters by the number of ways to arrange digits.

Sample Space

In probability theory, the sample space is the set of all possible outcomes of an experiment. For the license plate problem, it represents every possible configuration of letters and digits, and determining its size is key to computing the probability of selecting a specific plate.

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