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Combinatorics

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Moderate

Suit Distribution in a Bridge Hand

COMBIN-LJNL4W

In the game of bridge a player is dealt 13 cards from a standard deck of 52 cards. How many ways are there for a player to get at least 3 cards of each of the 4 suits?

A

$${13\choose 4}{13\choose 3}^3$$

B

$${4\choose 1}{13\choose 4}{13\choose 3}^3$$

C

$${52\choose 13}\cdot 4!\cdot (3!)^3$$

D

$${52\choose 13}{13\choose 4}{13\choose 3}^3$$

E

$${52\choose 13}{13\choose 4}{9\choose 3}{6\choose 3}{3\choose 3}$$