For each of the subsets of the two properties (a) and (b), count the number of four-digit numbers whose digits are either 1, 2, 3, 4, or 5.
(a) The digits are distinct.
(b) The number is even.
Note that there are four problems here: (1) when both conditions are met; (2) when only condition (a)
is met; (3) when only condition (b) is met; (4) when neither condition is met.