2. On a certain website, a password is 7 characters long. It can contain lowercase letters or

digits (0-9). Repetition of characters is allowed.

(a) A password must contain at least 1 lowercase letter and at least 1 digit. How many valid passwords are there?

(b) What is the probability that a randomly chosen password from (a) contains the string "prob"?

(c) Now suppose a password can be 7, 8, or 9 characters long (the same restrictions in (a) still apply). Now how many valid passwords are there?

(d) What is the probability that a randomly chosen password from (a) contains the digit '1'?