A standard 52 card playing deck assigns a unique combination of 13 ranks (2,3,4,5,6,7,8,9,10,J,Q,K,A) and 4 suits (Clubs, Diamonds, Hearts, Spades) to each card (13 4 = 52). Suppose 5 cards are selected at random. Derive the probability that each of the following events occurs.
(a) All cards are face cards (J,Q,K) of a single color (all black [spades or clubs] or all red [hearts or diamonds]).
(b) All suits are represented at least once.
(c) All ranks are distinct, and of a single color.
Carefully list the tasks used in the application of the rule of product.