The table below shows the probability of drawing various hands in a game of poker (Five Card Stud):

Suppose you draw fve hands of poker. (To simplify, assume you start with a new shuffled deck for each hand.) Use the binomial probability function to compute the probability that you will draw
a. Three of a kind exactly once in the fve hands.
b. Two pair exactly twice in the fve hands.
c. Nothing in all fve hands.
d. Two pair or better exactly once in the fve hands.

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Hand Royal flush Straight flush Four of a kind Full house Flush Straight Three of a kind Combinations Probability 0.00000154 0.00001385 0.00024010 0.00144058 0.00196540 392465 0.02112845 0.04753902 0.42256903 1,302,540 0.50117730 1.00000000 4 36 624 3,744 5,108 10,200 54,912 123,552 1,098,240 0.00 Two pair Pair Nothing TOTAL 2,598,960