A computer system uses passwords that contain exactly eight characters, and each character is one of the 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. Suppose that all passwords in Ω are equally likely. Determine the probability for each of the following:

(a) Password contains all lowercase letters given that it contains only letters

(b) Password contains at least 1 uppercase letter given that it contains only letters

(c) Password contains only even numbers given that is contains all numbers