Question

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.
474,552
6,169,176
49,353,408
133,784,560

Answer 1

Choose 2 hearts, 2 diamonds, 2 clubs, and 1 spade:
C(13,2)^3 · C(13,1) = 78^3 · 13 = 474,552 · 13 = 6,169,176.