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At a certain company, passwords must be from 3-5 syml

At a certain company, passwords must be from 3-5 syml

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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## Password Combinations and Probability ### Overview At a certain company, passwords must be 3–5 symbols long, composed of 26 uppercase letters, ten digits (0–9), and 14 symbols (!, @, #, $, %, ^, &, *, (, ), -, +, {, }). The following questions explore different aspects of password possibilities. ### (a) Passwords with Repetition Allowed - **Concept**: Calculate possible passwords when repetition is permitted. - **Process**: - There are ________ choices for each entry in the password. - Using the __________ method, the number of passwords of length \( n \) is ________. - Passwords can have length 3, 4, or 5. - Using the __________ method, calculate the total number of passwords with 3, 4, or 5 symbols: ________. ### (b) Passwords with No Repeated Symbols - **Hint**: When entering symbols, choices decrease by 1 for each additional symbol. - **Total Number**: - Calculate total passwords of lengths 3, 4, or 5 where each has no repeated symbol: ________. ### (c) Passwords with At Least One Repeated Symbol - Determine the total number of passwords having at least one repeated symbol: ________. ### (d) Probability of Repeated Symbols - **Question**: What is the probability of choosing a password with at least one repeated symbol? - **Answer**: ________% (rounded to the nearest tenth). This exercise helps understand the mathematical principles behind password generation and the impact of different constraints on potential combinations.
Transcribed Image Text:## Password Combinations and Probability ### Overview At a certain company, passwords must be 3–5 symbols long, composed of 26 uppercase letters, ten digits (0–9), and 14 symbols (!, @, #, $, %, ^, &, *, (, ), -, +, {, }). The following questions explore different aspects of password possibilities. ### (a) Passwords with Repetition Allowed - **Concept**: Calculate possible passwords when repetition is permitted. - **Process**: - There are ________ choices for each entry in the password. - Using the __________ method, the number of passwords of length \( n \) is ________. - Passwords can have length 3, 4, or 5. - Using the __________ method, calculate the total number of passwords with 3, 4, or 5 symbols: ________. ### (b) Passwords with No Repeated Symbols - **Hint**: When entering symbols, choices decrease by 1 for each additional symbol. - **Total Number**: - Calculate total passwords of lengths 3, 4, or 5 where each has no repeated symbol: ________. ### (c) Passwords with At Least One Repeated Symbol - Determine the total number of passwords having at least one repeated symbol: ________. ### (d) Probability of Repeated Symbols - **Question**: What is the probability of choosing a password with at least one repeated symbol? - **Answer**: ________% (rounded to the nearest tenth). This exercise helps understand the mathematical principles behind password generation and the impact of different constraints on potential combinations.
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