Bill has a set of 6 black cards and a set of 6 red cards. Each card has a number from 1 through 6, such that each of the numbers 1 through 6 appears on 1 black card and 1 red card. Bill likes to play a game in which he shuffles all 12 cards, 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?
(A) \frac{8}{33}
(B) \frac{62}{65}
(C) \frac{17}{33}
(D) \frac{103}{165}
(E) \frac{25}{33}![]()
(A) \frac{8}{33}
(B) \frac{62}{65}
(C) \frac{17}{33}
(D) \frac{103}{165}
(E) \frac{25}{33}