Val is a master of cryptography and her passwords are known to be impossible to hack. She uses a unique strategy to generate passwords - she generates a 12-character pass-word by selecting each character independently and uniformly at random from {a, b, . . . , z} {A, B, . . . , Z} {0, 1, . . . , 9}.

(a) What is the probability that exactly 4 of the characters are digits?

(b) What is the expected number of digits in a password?

(c) What is the variance of the number of digits in a password?