A computer password consists of eight characters. Replications are allowed.

a. How many different passwords are possible if each character may be any lowercase letter or digit?

b. How many different passwords are possible if each character may be any lowercase letter?

c. How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit?

d. A computer is generating passwords. The computer generates eight characters at random, and each is equally likely to be any of the 26 letters or 10 digits. Replications are allowed. What is the probability that the password will contain all letters?

e. A computer system requires that passwords contain at least one digit. If eight characters are generated at random, what is the probability that they will form a valid password?