A certain passcode is required to be a sequence of any 3 dig…
A certain passcode is required to be a sequence of any 3 digits chosen from the ten digits followed by 2 letter chosen from the set {a, b, c, d}. (1) How many passcodes are possible if repetition of digits and letters is allowed? (2) How many passcodes contain no repeated digits and no repeated letters? (3) How many passcodes are possible if repetition of digits is allowed but no repeated letters? (4) What is the probability that a passcode chosen at random has at least one repeated digit or one repeated letter, assuming that all passcodes are equally likely? (Please fill the blank with a numerical value in the form of m/n, where m and n are positive integers.) In (1), (2) and (3), please enter your answers as integers.