PLEASE ANSWER ALL THE QUESTIONS ABOVE AND I WILL RATE YOU

(a) A standard deck of 52 playing cards is shuffled and then dealt into 13 piles of 4 cards each. Prove that, regardless of how the deck is shuffled, there is always a way to select one card from each pile so that each of the 13 possible ranks (2,3,,10, Jack, King, Queen, Ace) occurs once. (b) Prove that any k-regular bipartite graph G=(AB,E) on n2 vertices (k1) has the following property: its edge set E can be written as the union of k edge-disjoint perfect matchings. (Hint: in class we proved that such a k-regular bipartite graph contains a perfect matching.) (c) Prove that in part (a) we can in fact go one step further: we can divide the cards into 4 groups of 13 cards each, where each group has one card from every pile, and one card from every rank