A computer system uses passwords that contain exactly eight characters, and each character is one of 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Suppose that all passwords in Ω are equally likely.

Determine the probability of each of the following:

(a) A

(b) B

(c) A password contains at least 1 integer.

(d) A password contains exactly 2 integers.