Bill has a small deck of 14 playing cards made up of only 2 suits of 7 cards each. Each of the 7 cards within a suit has a different value from 1 to 7; 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 4 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?  Choices:
A) 8/67
B) 61/130
C) 17/33
D) 63/143
E) 25/88
P(no pairs) = 12/13*10/12*8/11 = 80/143   P(at least one pair) = 1 - 80/143 = 63/143   The answer is 63/143.
<result>D</result>
Bill has a small deck of 14 playing cards made up of only 2 suits of 7 cards each. Each of the 7 cards within a suit has a different value from 1 to 7; 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 4 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?