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" ✓✓, the total number of passwords consisting of 4, 5, or 6 symbols is passwords may have length 4, 5, or 6, by the addition rule (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 X (b) How many passwords contain no repeated symbols? (Hint: In this case, 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 Because (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.) % Thus, the number of passwords with at least one repeated symbol is
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" ✓✓, the total number of passwords consisting of 4, 5, or 6 symbols is passwords may have length 4, 5, or 6, by the addition rule (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 X (b) How many passwords contain no repeated symbols? (Hint: In this case, 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 Because (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.) % Thus, the number of passwords with at least one repeated symbol is
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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do not put answers as scientific notation. if you do I will dislike. answer is an exact number and I need to know what I need to put down for finals.
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 ✓ ✓
passwords may have length 4, 5, or 6, by the addition rule
the number of passwords of length n is 50"
, the total number of passwords consisting of 4, 5, or 6 symbols is
(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
X.
(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
. Because
(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.)
%
. Thus, the number of passwords with at least one repeated symbol is
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