1. Find the number of different ways to draw a 4-of-a-kind hand from a standard 52 card deck, i.e. X X X X Y where the X's are four cards of the same rank (A to 2) and Y differs from X in rank. (Note: there are 4 suits per rank.) Let's think this through together.
(a) Suppose we pick the cards in order of X X X X Y.
How many ways can we pick the 1st card from the deck of 52 cards?
(b) Now if the 2nd card has to match the rank of the 1st card, how many ways can we pick the 2nd card from the remaining 51 cards in the deck?