a) A student can repeat an examination until it is passed, but is allowed to attempt the examination at most four times

a) A student can repeat an examination until it is passed, but is allowed to attempt the examination at most four times. List the elements of the sample space S, and the event E that the student passes.

b) If passwords can consist of eight letters, find the probability that a randomly chosen password will not have any repeated letters. A seven-letter password consists of case sensitive letters (52 in all) and the 10 digits. If a valid password must begin with a letter, and contain at least one digit, how many passwords are possible?