What I would do is:C(13,1)C(13,2)C(3,1)C(13,2)C(2,1)C(13,8)C(1,1).But I don't know if I need to choose specific suits for the doubleton cards and the remaining 8 cards.
Thanks!
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One spade card: 13 possibilities
Which doubleton suits: 3 possibilities: Which do we leave out?
Per doubleton suit there are C(13,2) = 78 possibilities.
For the remaining cards there are C(13,8) possibilities.
This gives a total of 39C(13,2)^2C(13,8).
This isn't the same as your answer: your answer is twice as large. This is beacuse you count the two doubleton suits as different.
wythagoras
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I don't understand what do you mean by" doubleton suits: 3 possibilities".And why we need to multiply by 39 in the answer? – JimfyWinsy May 02 '15 at 15:38
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You can have clubs and hearts doubleton suits, clubs and diamonds doubleton suits or hearts and diamonds doubleton suits. – wythagoras May 02 '15 at 15:39
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Oh,but does it influence the final results? – JimfyWinsy May 02 '15 at 15:41
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You count clubs+diamonds and diamonds+clubs as two different possibilities, while they are equal. (and the same for the other suits) – wythagoras May 02 '15 at 15:44
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Why you choose the spade from 39? – JimfyWinsy May 02 '15 at 16:08
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I don't, the 39 is 3*13. Read the answer carefully please. – wythagoras May 02 '15 at 16:10