4. In one variety of poker, players are dealt five cards from an ordinary deck of 52 cards.
(a) A full house in poker is a hand of five cards of one denomination and 3 cards of another denomination. Find the probability of a player being dealt a full house.
(b) Two pairs is a poker hand containing 2 cards of one denomination, another 2 cards of a second denomination, and a fifth cards of a third dimension. Find the probability of a player being dealt two pairs.
5. Given n marbles where k of the marbles are black and the rest are white, a game is played as follows. You choose two marbles at random, and you win the game if the marbles are of different colors. Prove that for a fixed n, you have the highest probability of winning when k = n/2 (for even values of n) and when k = (n (plus or minus) 1)/2 (for odd values of n)