A standard deck of 52 cards contains 13 cards with hearts, 13 with diamonds, 13 with clubs, and 13 with spades. How many 7-card hands are possible with 2 hearts, 2 diamonds, 2 clubs, and 1 spade? Assume that the order of the cards does not matter, and use the formula for combinations to find your answer.

Choose 2 of the 13 hearts, 2 of the 13 diamonds, 2 of the 13 clubs, and 1 of the 13 spades. By the combination formula, the number of hands is C(13,2) × C(13,2) × C(13,2) × C(13,1) = 78 × 78 × 78 × 13 = 6,169,176. Therefore, the correct choice is 6,169,176.

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