problem 1)A) Assume you are taking a multiple-choice test comprising 30 problems, each of which has 5 choices (A,B,C,D,E). How many different ways are there to complete test, if you are required to answer every problem? How many various ways are there to complete test if you leave at least one problem blank?
B) Assume you are trying to improve 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):
a) Should be 8-12 characters long (inclusive)
b) Uppercase letters, lowercase letters, and digits are allowed
c) Should contain exactly one uppercase letter
d) Should contain exactly one digit
You devise a new set of password constraints, as follows:
a) Should be exactly 9 characters
b) Uppercase letters, lowercase letters, digits, underscores, and hyphens are allowed
c) Should contain at least one uppercase letter
d) Should contain at least one digit
e) Should 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?