SOLUTION: This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen from the deck.
How many hands contain exactly 3 jacks?
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-> SOLUTION: This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen from the deck.
How many hands contain exactly 3 jacks?
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Question 1132949: This exercise refers to a standard deck of playing cards. Assume that 5 cards are randomly chosen from the deck.
How many hands contain exactly 3 jacks? Found 2 solutions by math_helper, rothauserc:Answer by math_helper(2461) (Show Source):
The number of three of kind hands (where three cards match and the other two do not match) is:
The factors are:
(selection of rank)*(#arrangments of three matching cards)*(selection of nonmatching two cards)*(number of arrangements of those two)
The number of full houses (three matching and other two cards match):
Thus the total number of hands where three cards match, regardless of the remaining two cards is 54912+3744 = 58656
But, the problem only asks about jacks, which means the above number must be divided by (13C1) since the rank is chosen for you:
58656/13 = 4512
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The number of hands with exactly three jacks is
(This also answers the question about how many hands have exactly three queens, as the rank does not matter).
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Thanks tutor rothauserc! Yes, that approach is much more direct! I had poker hands in mind and went the round-about way. For the student, the first factor in tutor rothauserc's solution is the number arrangments of 3 jacks out of 4, and the 2nd factor is the number of arrangements of the remaining 2 cards out of 48. What I like about this website is I get to learn too :-)
You can put this solution on YOUR website! A standard deck of playing cards consists of 52 cards
:
nCr = n! /(r! * (n-r)!)
:
4C3 * 48C2 = 4512 hands contain exactly 3 jacks
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