A.) Suppoose youre taking a multiple-choice test comprising 30 questions, each o
ID: 3545567 • Letter: A
Question
A.) Suppoose youre taking a multiple-choice test comprising 30 questions, each of which has 5 choices (A,B,C,D,E). How many different ways are there to complete the test, if you are required to answer every question? How many different ways are there to complete the test if you leave at least one question blank?
B.) Suppose youre trying to improve the password system for the University of Memphis. At the moment, passwords have the following restrictions (not really, but just for the purposes of this exercise):
? Must be 8-12 characters long (inclusive)
? Uppercase letters, lowercase letters, and digits are allowed
? Must contain exactly one uppercase letter
? Must contain exactly one digit
You devise a new set of password constraints, as follows:
? Must be exactly 9 characters
? Uppercase letters, lowercase letters, digits, underscores, and hyphens are allowed
? Must contain at least one uppercase letter
? Must contain at least one digit
? Must contain exactly one special character (underscore or hyphen)
Which password scheme is more secure against brute-force attacks? In your opinion, which one is better for end-users and why?
Explanation / Answer
A) (i) every question can be attempted in 5 ways therefore total no. of ways = 5*5*5*5*5......... 30 times = 5^30
(ii) no of ways to leave at least one queston blank = total no. - when question is left = 6^30 - 5^30
here total ways is 6^30 because every question can be answered in 6 ways(A,B,C,D,E or leaving the queston).
B) second sheme is more secure against brute force attacke as well as better for end users because in second case the total number of possibilities of passwords that can be made are higher. So the possibility of merely guessing one's answer decreases thus making it more secure.
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