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Math·Problem-Solving and Data Analysis·Probability and conditional probability

hard

A standard deck of playing cards has 52 cards, with 13 cards in each of four suits: clubs, diamonds, hearts, and spades. Each suit has three face cards (jack, queen, and king). For a particular card game, a player is dealt a hand of five cards from a standard deck. The number of distinct hands containing exactly three face cards is given by the expression       .

A

$\left(\genfrac{}{}{0ex}{}{12}{3}\right)$

B

$\left(\genfrac{}{}{0ex}{}{12}{3}\right)\left(\genfrac{}{}{0ex}{}{40}{2}\right)$

C

$\left(\genfrac{}{}{0ex}{}{52}{3}\right)\left(\genfrac{}{}{0ex}{}{49}{2}\right)$

D

$\left(\genfrac{}{}{0ex}{}{13}{3}\right)(4)$