Question

A computer system uses passwords that are exactly seven characters, and each character is one of the 26 letters $(a-z)$ or 10 integers $(0-9)$. Uppercase letters are not used. (a) How many passwords are possible?

Name: Problem 225, Chapter 2: Applied Statistics and Probability for Engineers
Uploaded: 2021-08-09T16:59:35-08:00
Duration: 1 min 49 s
Channel: Maxime Rossetti
Description: A computer system uses passwords that are exactly seven characters, and each character is one of the 26 letters (a-z) or 10 integers (0-9). Uppercase letters are not used. (a) How many passwords are possible?

   A computer system uses passwords that are exactly seven characters, and each character is one of the 26 letters $(a-z)$ or 10 integers $(0-9)$. Uppercase letters are not used.
(a) How many passwords are possible?

Applied Statistics and Probability for Engineers

Douglas C.… 6th Edition

Chapter 2, Problem 225

Instant Answer

Solved by Expert Maxime Rossetti

08/09/2021

Step 1

Each character can be one of the 26 lowercase letters (a-z) or one of the 10 integers (0-9). This gives us a total of 36 possible characters for each position in the password. Show more…

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A computer system uses passwords that are exactly seven characters, and each character is one of the 26 letters $(a-z)$ or 10 integers $(0-9)$. Uppercase letters are not used. (a) How many passwords are possible?

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Key Concepts

Multiplication Principle

This principle states that if there are several independent choices to be made, the total number of possible outcomes is the product of the number of options at each decision step. In the context of password creation, where each character position is chosen independently from a fixed set of characters, the multiplication principle allows us to calculate the total number of possible passwords by multiplying the number of choices available for each character position.

Permutations with Repetition

This concept applies when the order of items matters and selections for each position can be repeated. In generating passwords, each character slot can be filled by any of the available characters (letters and numbers) without restrictions on reusing them. The total count is obtained by raising the number of available characters to the power equal to the number of positions, showcasing the use of exponentiation in counting repeated selections.

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