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nikdorinn [45]
3 years ago
7

A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactl

y 6 face cards.
Mathematics
1 answer:
Andrew [12]3 years ago
6 0

Answer: \dfrac{^{12}C_{6}\times^{40}C_3}{^{52}C_9} or  \dfrac{228}{91885} .

Step-by-step explanation:

Given : A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards.

The total number of cards in a deck 52

Number of faces cards in a deck = 12

Number of cards not face cards = 40

The total number of combinations of drawing 9 cards out of 52 cards = ^{52}C_9

Now , the combination of 9 cards such that exactly 6 of them are  face cards =  ^{12}C_{6}\times^{40}C_3

Now , the probability that the hand contains exactly 6 face cards will be :-

\dfrac{^{12}C_{6}\times^{40}C_3}{^{52}C_9}

=\dfrac{\dfrac{12!}{6!6!}\times\dfrac{40!}{3!37!}}{\dfrac{52!}{9!\times43!}}\ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{228}{91885}

Hence, the probability that the hand contains exactly 6 face cards. is  \dfrac{228}{91885} .

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