SOLUTION: A poker hand consisting of 8 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactly 2 face cards. Leave your answer as a reduced fr

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Question 1204246: A poker hand consisting of 8 cards is dealt from a standard deck of 52 cards.
Find the probability that the hand contains exactly 2 face cards. Leave your answer as a reduced fraction.
The probability is
.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

A standard deck of 52 cards has 12 face cards and 40 cards that are not face cards.


The total number of groups of 8 cards is  C%5B52%5D%5E8 = 752538150.  It is the full set of events.


Of them, favorable set consists of groups that have 2 face cards, which we can combine in  C%5B12%5D%5E2 = 66 ways,
and 8-2 = 6 non-face cards, which we can combine in  C%5B40%5D%5E6 = 3838380 ways.



So, the probability under the question is  P = %2866%2A3838380%29%2F752538150.


The reduced fraction is  P = 30932%2F91885.    ANSWER

Solved.