At a certain company, passwords must be from 4-6 symbols long and composed from the 26 uppercase letters of the Roman alphabet, the ten digits 0-9, and the 14 symbols !, @, #, $, %, ^, &, *, (, ), -, +, {, and ). Use the methods illustrated in Example 9.3.2 and Example 9.3.3 to answer the following questions. (a) How many passwords are possible if repetition of symbols is allowed? If repetition is allowed, there are 50 v choices for each entry in the password. So, by the multiplication rule : , the number of passwords of length n is 50 x . Because passwords may have length 4, 5, or 6, by the addition rule 9v , the total number of passwords consisting of 4, 5, or 6 symbols is 15943750000 (b) How many passwords contain no repeated symbols? (Hint: In this case, each additional symbol is entered.) symbols are entered into a password one by one, the number of choices for each entry decreases by 1 as The total number of passwords consisting of 4, 5, or 6 symbols, each of which has no repeated symbol, is 11701082400 (c) How many passwords have at least one repeated symbol? . Thus, the number of passwords with a The number of passwords with at least one repeated symbol plus the number of passwords with no repeated symbols is 15943750000 least one repeated symbol is 4242667600 (d) What is the probability that a password chosen at random has at least one repeated symbol? (Round your answer to the nearest tenth of a percent.) 26.6 %
At a certain company, passwords must be from 4-6 symbols long and composed from the 26 uppercase letters of the Roman alphabet, the ten digits 0-9, and the 14 symbols !, @, #, $, %, ^, &, *, (, ), -, +, {, and ). Use the methods illustrated in Example 9.3.2 and Example 9.3.3 to answer the following questions. (a) How many passwords are possible if repetition of symbols is allowed? If repetition is allowed, there are 50 v choices for each entry in the password. So, by the multiplication rule : , the number of passwords of length n is 50 x . Because passwords may have length 4, 5, or 6, by the addition rule 9v , the total number of passwords consisting of 4, 5, or 6 symbols is 15943750000 (b) How many passwords contain no repeated symbols? (Hint: In this case, each additional symbol is entered.) symbols are entered into a password one by one, the number of choices for each entry decreases by 1 as The total number of passwords consisting of 4, 5, or 6 symbols, each of which has no repeated symbol, is 11701082400 (c) How many passwords have at least one repeated symbol? . Thus, the number of passwords with a The number of passwords with at least one repeated symbol plus the number of passwords with no repeated symbols is 15943750000 least one repeated symbol is 4242667600 (d) What is the probability that a password chosen at random has at least one repeated symbol? (Round your answer to the nearest tenth of a percent.) 26.6 %
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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Transcribed Image Text:At a certain company, passwords must be from 4-6 symbols long and composed from the 26 uppercase letters of the Roman alphabet, the ten digits 0-9, and the 14 symbols !, @, #, $,
%, ^, &, *, (, ), -, +, {, and }. Use the methods illustrated in Example 9.3.2 and Example 9.3.3 to answer the following questions.
(a) How many passwords are possible if repetition of symbols is allowed?
If repetition is allowed, there are 50
choices for each entry in the password. So, by the multiplication rule
, the number of passwords of length n is
50
X . Because passwords may have length 4, 5, or 6, by the addition rule
, the total number of passwords consisting of 4, 5, or 6 symbols is
15943750000
(b) How many passwords contain no repeated symbols? (Hint: In this case, if symbols are entered into a password one by one, the number of choices for each entry decreases by 1 as
each additional symbol is entered.)
The total number of passwords consisting of 4, 5, or 6 symbols, each of which has no repeated symbol, is 11701082400
(c) How many passwords have at least one repeated symbol?
The number of passwords with at least one repeated symbol plus the number of passwords with no repeated symbols is 15943750000
. Thus, the number of passwords with at
least one repeated symbol is 4242667600
(d) What is the probability that a password chosen at random has at least one repeated symbol? (Round your answer to the nearest tenth of a percent.)
26.6
%
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