Zip Codes. In the United States a five-digit zip code is...

Name: Problem 29, Chapter 12: Algebra and Trigonometry
Uploaded: 2021-06-24T16:03:20-08:00
Duration: 1 min 30 s
Channel: James Kiss
Description: Zip Codes. In the United States a five-digit zip code is used to route mail. How many five-digit zip codes are possible? (All numbers can be used.) If 0 s were eliminated from the first and last digits, how many possible zip codes would there be?

Zip Codes. In the United States a five-digit zip code is used to route mail. How many five-digit zip codes are possible? (All numbers can be used.) If 0 s were eliminated from the first and last digits, how many possible zip codes would there be?

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Key Concepts

Fundamental Counting Principle

This principle states that if there are a certain number of ways to perform one action and another number of ways to perform a subsequent independent action, then the total number of ways to perform both actions is the product of the two. In problems where you determine the total number of outcomes by multiplying the number of options in each step, this principle is used.

Permutations with Repetition

Permutations with repetition involve calculating the number of sequences (or arrangements) when each position in the sequence can independently choose from the same set of options, with repetitions allowed. This concept is applied to problems where elements can be reused in different positions, such as in generating numerical sequences.

Restrictions in Combinatorics

Restrictions in combinatorics refer to conditions that limit or modify the choices available for certain positions in a sequence. This concept is critical when specific digits or positions have rules that exclude certain values, which changes the total number of valid configurations compared to the unrestricted scenario.

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