SOLUTION: how many 13 card hands are there that have exactly eight spades and no diamonds?

Question 1050194: how many 13 card hands are there that have exactly eight spades and no diamonds?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!


Choose the 8 spades from the 13 spades in 13C5 ways
For each of those, choose the remaining 
 5 from the 26 hearts and clubs in 26C5 ways.

So there are (13C8)(26C5) "successful" hands.

That's the numerator of the desired probability.

The denominator is the number of 13-card hands from
the entire deck of 52.  That's 52C13

Answer:  

That fraction was reduced by dividing top and bottom by 460.

As a decimal that's 0.000133318192..., a very low probability.

Edwin

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