The captain of a darts team is trying to arrange an evening match for next Monday, Tuesday, Wednesday or Thursday. He hopes that the leading players, A, B, C and D, will all be free on one of these evenings. In fact each of the four players has arranged an engagement for exactly one of the four evenings. Assuming that each player is equally likely to have chosen any one of the four evenings, and that their choices are independent, find the probability that

(a) A and B have both chosen Monday evening,

(b) either C or D (or both) has chosen Monday evening,

(c) the four players have chosen four different evenings,

(d) there will be at least one evening when all four players are free. (NEAB)