Bill has a small deck of 10 playing cards made up of only 2 suits of 5 cards each. Each of the 5 cards within a suit has a different value from 1 to 5; thus, there are 2 cards in the deck that have the same value. Bill likes to play a game in which he shuffles the deck, turns over 5 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
Pick: A) 25/33 B) 35/43 C) 45/53 D) 55/63 E) 65/73
P(no pairs) = 8/9*6/8*4/7*2/6 = 8/63   P(at least one pair) = 1 - 8/63 = 55/63   The answer is 55/63.
<result>D</result>
Bill has a small deck of 10 playing cards made up of only 2 suits of 5 cards each. Each of the 5 cards within a suit has a different value from 1 to 5; thus, there are 2 cards in the deck that have the same value. Bill likes to play a game in which he shuffles the deck, turns over 5 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?