Postal Zip Codes The U.S. Postal Service is encouraging the...

Name: Problem 50, Chapter 8: Finite Mathematics and Calculus with Applications
Uploaded: 2020-05-05T18:51:53-08:00
Duration: 53 s
Channel: Foster Wisusik
Description: Postal Zip Codes The U.S. Postal Service is encouraging the use of 9-digit zip codes in some areas, adding 4 digits after the usual 5-digit code. How many such zip codes are possible with no restrictions?

Postal Zip Codes The U.S. Postal Service is encouraging the use of 9-digit zip codes in some areas, adding 4 digits after the usual 5-digit code. How many such zip codes are possible with no restrictions?

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Key Concepts

Fundamental Counting Principle

This principle states that if there are several tasks to be performed consecutively and each task can be done in a certain number of ways independent of the previous tasks, then the total number of outcomes is the product of the number of ways each task can be performed. In counting problems involving digits or choices, this principle is key to finding the total number of combinations.

Exponential Notation

Exponential notation is a mathematical shorthand used to represent repeated multiplication of the same number. In counting problems where each digit has a fixed number of possibilities, the total number of outcomes can often be expressed as a base (the number of options per digit) raised to a power (the number of digits), simplifying calculations and the representation of large numbers.

Place Value and Digit Independence

In problems involving sequences of digits, such as zip codes, each digit is considered independent and can be selected without influencing the others. The concept of place value explains the significance of each digit's position in the sequence, and when digits are chosen independently, it facilitates the application of the Fundamental Counting Principle to compute the total possible numbers.

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