Consider an ordinary deck of 52 playing cards with four suits (hearts, spades, diamonds, clubs) and 13 ranks in each suit (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K). You pick cards from the deck one at a time without replacement. What is the minimum number of cards you must pick in order to guarantee that you get: a) a pair of any rank, b) a pair of aces, and c) all four aces. 5. (2 pts) Consider the binomial theorem to expand (2x + 4y). What is the coefficient of the xy term? You must illustrate use of the binomial theorem for full credit.