Sports and Leisure Texas hold 'em poker has become very popular in gambling casinos and is seen on ESPN and the Travel Channel. In November 2012, Greg Merson won the World Series of Poker in Las Vegas and a cool $8.53 million. The game is played with a standard 52-card deck, and starts with each player being dealt two (random) cards face down (hole cards).
There is a round of betting, the dealer then flips three cards face up (the flop), betting, one card is flipped (the turn), betting, a fifth card is flipped (the river), and more betting. Let's focus on the two hole cards, called a (pre-flop) hand, in this problem.
a. How many (two-card, pre-flop) hands are possible in Texas hold 'em?
b. What is the probability that a pre-flop hand consists of two aces?
c. What is the probability that a pre-flop hand consists of a pair, that is, two cards of the same rank?
d. What is the probability that a pre-flop hand consists of two cards of the same suit?