3. 25 points To sign up for a new COVID-19 contact tracing app, users are asked to pick a password of length 8, with the following guidelines. The password must have . exactly 4 upper-case letters (can be chosen with replacement ) from {A, B, - -. , Z} . exactly 2 lower-case letters (can be chosen with replacement ) from {a, b, - - - , z} . exactly 2 special characters (chosen without replacement ) from the following list { #, $, %, &, !, @} (a) How many distinct passwords are possible? (b) Suppose there are N users that sign up for the app. Each user independently picks a valid password at random. What is the probability that none of the users share the same password