SOLUTION: Find the number of possible 5-card hands tht contain the cards specified: 1. 2 of one kind, 2 of a second kind, and 1 other card (the answer is 123,552 i just dont know how to get

Question 745174: Find the number of possible 5-card hands tht contain the cards specified:
1. 2 of one kind, 2 of a second kind, and 1 other card (the answer is 123,552 i just dont know how to get the answer)
2. 3 face cards (kngs, queensm or jacks) of the same suit and 2 other cards(none of which are face cards) (answer is 3120 just dont know how to get the answer)
Thanks SO much!!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the number of possible 5-card hands tht contain the cards specified:
1. 2 of one kind, 2 of a second kind, and 1 other card (the answer is 123,552 i just dont know how to get the answer)
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Pick a card type: 13 ways
Pick 2 of that type: 13C2
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Pick a different card type: 12 ways
Pick 2 of that type: 13C2
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Pick a 3rd card type: 11 ways
Pick 1 of that type: 13 ways
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Ans: (13*12*11)*(13C2*13C2*13) = a big number but not 123,552
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2. 3 face cards (kngs, queens or jacks) of the same suit and 2 other cards(none of which are face cards) (answer is 3120 just dont know how to get the answer)
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If the KQJ are of the same suit there are 4 ways to get those 3 cards.
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There are 40 non-face cards:
There are 40C2 = (40*39)/(1*2) = 780 ways to get the 2 non-face cards
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Ans: 4*780 = 3120
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Cheers,
Stan H.
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