document.write( "Question 1050194: how many 13 card hands are there that have exactly eight spades and no diamonds? \n" ); document.write( "

Algebra.Com's Answer #666412 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Choose the 8 spades from the 13 spades in 13C5 ways\r\n" );
document.write( "For each of those, choose the remaining \r\n" );
document.write( " 5 from the 26 hearts and clubs in 26C5 ways.\r\n" );
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document.write( "So there are (13C8)(26C5) \"successful\" hands.\r\n" );
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document.write( "That's the numerator of the desired probability.\r\n" );
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document.write( "The denominator is the number of 13-card hands from\r\n" );
document.write( "the entire deck of 52.  That's 52C13\r\n" );
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document.write( "Answer:  \r\n" );
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document.write( "That fraction was reduced by dividing top and bottom by 460.\r\n" );
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document.write( "As a decimal that's 0.000133318192..., a very low probability.\r\n" );
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document.write( "Edwin

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