We shuffle a standard deck of cards, obtaining a permutation that is uniform over all 52! possible permutations. Find the probability of the following events. (a) The first two cards include at least one ace. (b) The first five cards include at least one ace. (c) The first two cards are a pair of the same rank. (d) The first five cards are all diamonds. (e) The first five cards form a full house (three of one rank and two of another rank)