Question

A U.S. postal zip code is a five-digit number. a) How many zip codes are possible if any of the digits 0 to 9 can be used? b) If each post office has its own zip code, how many possible post offices can there be?

Name: Problem 39, Chapter 11: Algebra and Trigonometry
Uploaded: 2020-07-15T08:29:24-08:00
Duration: 1 min 26 s
Channel: Ankit Gupta
Description: A U.S. postal zip code is a five-digit number. a) How many zip codes are possible if any of the digits 0 to 9 can be used? b) If each post office has its own zip code, how many possible post offices can there be?

   A U.S. postal zip code is a five-digit number.
a) How many zip codes are possible if any of the digits 0 to 9 can be used?
b) If each post office has its own zip code, how many possible post offices can there be?

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 11, Problem 39

Instant Answer

Solved by Expert Ankit Gupta

07/15/2020

Step 1

S. postal zip code is a five-digit number. Each digit can be any number from 0 to 9. Therefore, we have 10 choices for each digit. Show more…

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A U.S. postal zip code is a five-digit number. a) How many zip codes are possible if any of the digits 0 to 9 can be used? b) If each post office has its own zip code, how many possible post offices can there be?

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Key Concepts

Fundamental Counting Principle

This principle states that if there are multiple stages of selection and each stage has a certain number of independent choices, the total number of outcomes is the product of the number of choices at each stage. It allows us to systematically calculate the total number of combinations by multiplying the number of possibilities for each digit or decision.

Permutations with Repetition

When elements, such as digits, can be repeated across positions, the total number of outcomes is determined by raising the number of available options to the power corresponding to the number of positions. In the context of numerical codes, this means if each digit can be chosen from a fixed set independently, you multiply the number of choices per digit for the total count.

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