Brute force password guessing. Each of the following is a di↵erent kind of password. An attacker can always try to bypass password security by guessing every possible password that might exist. In the worst case (for the attacker), the correct password is the last one that they guess. So increasing the number of potential passwords makes password protection more e↵ective. For each password type, compute the number of passwords of that type that exist. Justify your answers (show your work). (c) Eight lower-case letters, upper-case letters, or digits. (d) Nine letters.

Give definitions for three distinct functions g1(n),g2(n), and g3(n) that are members of the set O(n3).