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Suppose that a deck of 25 cards contains 12 red cards. Suppose also that the 25 cards are distributed in a random manner to three players A, B, and C in such a way that player A receives 10 cards, player B receives 8 cards, and player C receives 7 cards. Determine the probability that player A will receive 6 red cards, player B will receive 2 red cards, and player C will receive 4 red cards.

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