License Plates. In a particular state, there are six...

License Plates. In a particular state, there are six characters in a license plate: three letters followed by three numbers. If 0 s and 1 s are eliminated from possible numbers and $\mathrm{Os}$ and Is are eliminated from possible letters, how many different license plates can be made?

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Key Concepts

Permutations with Repetition

This concept applies to situations where items are arranged in an order and each position in the arrangement can be filled by any of the available choices, even if the same choice is used more than once. It is especially useful in problems where the order matters and choices are made repeatedly from a limited set of options.

Restricted Choices in Combinatorics

Many counting problems impose constraints that limit the choices available for each selection. Understanding how to handle these restrictions—such as excluding certain values from a set—is essential for calculating correct outcomes in problems that involve specific rules or limitations in the allowed elements.

Fundamental Counting Principle

This principle states that if there are several independent events, the total number of outcomes is the product of the number of choices available for each event. It is a foundational concept in combinatorics used to systematically count the number of possible outcomes in multi-step processes.

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