Five Card Draw is one of most basic forms of poker, and it’s the kind of poker you’re used to seeing in movies and on TV. This game has been around for a long time, and has been played in countless home games and card rooms across the nation. Play begins with each player being dealt five cards, one at a time, all face down. The remaining deck is placed aside, often protected by placing a chip or other marker on it. Players pick up the cards and hold them in their hands, being careful to keep them concealed from the other players, then a round of betting occurs. Some combinations of five-card hand have special names such as full house, royal flush, four of a kind, etc.

Let`s find the probabilities of some 5-card combinations. Order of the drawn card does not matter. Enter your answer in decimal notation of a percent rounded to SEVEN decimal places.

a) A flush is a poker hand, where all five cards are of the same suit, but not in sequence. Find the probability of getting a 5-card poker hand containing all hearts.

b) Four of a kind, also known as quads, is a poker hand, that contains all four cards of one rank and any other (unmatched) card. Find the probability of getting a 5-card poker hand containing four Aces.

c) Find the probability of getting a 5-card poker hand containing any “four of a kind”. Hint: think, how many kinds are in the standard 52-card deck.

d) Three of a kind and a pair is a poker hand, that contains three cards of one rank and two cards of another (unmatched) rank. Find the probability of getting a 5-card poker hand containing three Queens and two Jacks.

e) Find the probability of getting a 5-card poker hand containing any “three of a kind and a pair”.

f) Find the probability of getting a 5-card poker hand containing 2 Kings, 2 Queens, and 1 Jack.

g) Compute the number of a 5-card poker hands containing 2 hearts, 2 diamonds, and 1 spade.