Question

Use any method described in this section to solve each problem. A briefcase has 2 locks. The combination to each lock consists of a 3 -digit number, where digits may be repeated. How many combinations are possible? (Hint: The word combination is a misnomer. Lock combinations are permutations where the arrangement of the numbers is important.)

Name: Problem 71, Chapter 11: Precalculus
Uploaded: 2021-06-05T09:42:03-08:00
Duration: 1 min 46 s
Channel: Km Neeraj
Description: Use any method described in this section to solve each problem. A briefcase has 2 locks. The combination to each lock consists of a 3 -digit number, where digits may be repeated. How many combinations are possible? (Hint: The word combination is a misnomer. Lock combinations are permutations where the arrangement of the numbers is important.)

   Use any method described in this section to solve each problem.
A briefcase has 2 locks. The combination to each lock consists of a 3 -digit number, where digits may be repeated. How many combinations are possible? (Hint: The word combination is a misnomer. Lock combinations are permutations where the arrangement of the numbers is important.)

Precalculus

Margaret L. Lial,… 6th Edition

Chapter 11, Problem 71

Instant Answer

Solved by Expert Km Neeraj

06/05/2021

Step 1

Since the digits can be repeated, for each digit in the combination, we have 10 choices (0 to 9). Show more…

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Use any method described in this section to solve each problem. A briefcase has 2 locks. The combination to each lock consists of a 3 -digit number, where digits may be repeated. How many combinations are possible? (Hint: The word combination is a misnomer. Lock combinations are permutations where the arrangement of the numbers is important.)

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Key Concepts

Fundamental Counting Principle

The Fundamental Counting Principle is the idea that if there are several independent choices to be made in sequence, the total number of outcomes is the product of the number of options available at each stage. This principle is crucial for determining the total number of possible results in a situation where multiple selections or stages are involved.

Permutations with Repetition

Permutations with Repetition refer to arrangements where the order of elements is important and elements can be repeated. In situations like forming numbers or codes, each position can be filled independently from a given set of choices, leading to a total number determined by multiplying the number of options for each position.

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