A typical automobile license plate in New York contains three letters followed by three digits.

step 1 For problem 23, we have to figure out how many ways California can have different license plates

A typical automobile license plate in New York contains...

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Key Concepts

Fundamental Counting Principle

This principle states that if there are several stages in an event and each stage can occur in a number of ways, the total number of outcomes is the product of the number of ways each stage occurs. It forms the backbone of solving combinatorial problems by enabling the multiplication of choices across successive positions.

Permutations with Repetition

When elements can be repeated, each position in a sequence is treated independently from the others. This means that if an element is allowed to appear multiple times, the number of possible outcomes for that position remains constant regardless of previous selections, which simplifies the counting process.

Handling Constraints in Counting Problems

Many combinatorial problems include specific restrictions that limit the possible outcomes for certain positions. Applying constraints—such as fixing a particular digit in the first position—requires explicitly setting the number of options for that position before applying the fundamental counting principle to the remaining positions.

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