Problem 1. Let's consider the number of possibilities for a password. The following characters are allowed in our passwords: 26 lowercase letters ('a' to 'z'), 26 uppercase letters ('A' to 'Z'), and 10 digits ('0' to '1'). (a) How many possible password combinations are there of 8 to 12 characters? (This includes passwords of length 8 and 12.) (b) Suppose these passwords are no longer case sensitive. For example, 'a' and 'A' are no longer viewed as distinct characters. Now how many distinct possible password combinations are there? (c) Now, suppose our passwords are case sensitive again. Suppose passwords must be exactly 8 characters long and have exactly 1 number. How many password combinations are possible?
Problem 1. Let's consider the number of possibilities for a password. The following characters are allowed in our passwords: 26 lowercase letters ('a' to 'z'), 26 uppercase letters ('A' to 'Z'), and 10 digits ('0' to '1'). (a) How many possible password combinations are there of 8 to 12 characters? (This includes passwords of length 8 and 12.) (b) Suppose these passwords are no longer case sensitive. For example, 'a' and 'A' are no longer viewed as distinct characters. Now how many distinct possible password combinations are there? (c) Now, suppose our passwords are case sensitive again. Suppose passwords must be exactly 8 characters long and have exactly 1 number. How many password combinations are possible?
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:Problem 1. Let's consider the number of possibilities for a password.
The following characters are allowed in our passwords: 26 lowercase letters ('a' to 'z'), 26 uppercase
letters ('A' to 'Z'), and 10 digits ('0' to '1').
(a) How many possible password combinations are there of 8 to 12 characters? (This includes passwords
of length 8 and 12.)
(b) Suppose these passwords are no longer case sensitive. For example, 'a' and 'A' are no longer viewed
as distinct characters. Now how many distinct possible password combinations are there?
(c) Now, suppose our passwords are case sensitive again. Suppose passwords must be exactly 8 characters
long and have exactly 1 number. How many password combinations are possible?
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