An old zip code in the United States consists of five digits. Find the total number of possible

step 1 If we're thinking about the zip codes, a five -digit zip code, first, assuming that all numbers

An old zip code in the United States consists of five...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Fundamental Counting Principle

This principle states that if an event can be broken down into a sequence of independent stages, then the total number of outcomes is the product of the number of ways each stage can occur. It is used to calculate the total possibilities when constructing sequences like numerical codes by multiplying the number of choices at each digit position.

Counting with Constraints

Counting with constraints involves modifying the number of outcomes at one or more stages based on given limitations, such as fixing the first digit of a sequence. When one digit is predetermined, the number of choices for that position is reduced, and this must be accounted for when applying the counting principles to the entire sequence.

Permutation with Repetition

In permutation with repetition, elements (such as digits) can be reused in different positions. Even when a constraint fixes one digit, the remaining positions can independently choose from the available set, and the overall count is found by raising the number of choices for each free position to the power corresponding to its frequency.

Transcript

Please give Ace some feedback