Question

Use the Fundamental Counting Principle. A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of four digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?

Name: Problem 27, Chapter 3: Elementary Statistics: Picturing the World
Uploaded: 2020-10-15T18:33:45-08:00
Duration: 54 s
Channel: Yingtai Xiao
Description: Use the Fundamental Counting Principle. A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of four digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?

   Use the Fundamental Counting Principle.
A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of four digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?

Elementary Statistics: Picturing the World

Ron Larson, Betsy… 6th Edition

Chapter 3, Problem 27

Instant Answer

Solved by Expert Yingtai Xiao

10/15/2020

Step 1

Since we have digits from 0 to 9, which gives us 10 choices, but the first digit cannot be zero, we are left with 9 choices. So, the total number of choices for the first digit is 9. Show more…

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Use the Fundamental Counting Principle. A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of four digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?

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Key Concepts

Fundamental Counting Principle

The Fundamental Counting Principle states that if there are several stages to a process, and each stage has a certain number of independent choices, then the total number of outcomes is the product of the number of choices at each stage. This principle is the core method for solving problems that involve counting the number of ways an event can occur when multiple independent options are involved.

Counting with Restrictions

Counting with Restrictions involves situations where certain conditions limit the possible outcomes at one or more stages of a counting problem. These restrictions, such as a digit not being allowed to be zero or needing to be even, require careful adjustment in calculating the number of valid choices. Understanding how restrictions affect individual stages ensures that the overall count accurately reflects the specific conditions imposed by the problem.

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