document.write( "Question 354612: Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards.\r
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Algebra.Com's Answer #253373 by Edwin McCravy(20059)\"\" \"About 
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document.write( "Find the probability of the following card hands from a 52-card deck.\r\n" );
document.write( "In poker, aces are either high or low. A bridge hand is made up of 13 cards.\r\n" );
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document.write( "In bridge, exactly 3 kings and exactly 3 queens\r\n" );
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document.write( "There are 4 kings, 4 queens and 44 cards that are neither.\r\n" );
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document.write( "So to have a successful hand, we must have 3 kings, 3 queens and 7 cards that\r\n" );
document.write( "are neither kings nor queens.\r\n" );
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document.write( "We cam pick the 3 kings \"4 choose 3\" or 4C3 ways.\r\n" );
document.write( "For each of those 4C3 ways to pick the 3 kings we can pick the 3 queens any of\r\n" );
document.write( "\"4 choose 3\" ways. So far we have 4C3*4C3\r\n" );
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document.write( "Now for each of those 4C3*4C3 ways to pick the 3 kings and queens, we\r\n" );
document.write( "must choose the other 7 cards from the 44 cards that are neither kings nor\r\n" );
document.write( "queens.  So the number of possible successful hands is \r\n" );
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document.write( "4C3*4C3*44C7\r\n" );
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document.write( "The denominator is the number of ways to pick any 13 cards from the\r\n" );
document.write( "52, so that's 52C13\r\n" );
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document.write( "So the desired probability is\r\n" );
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document.write( "4C3*4C3*44C7\r\n" );
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document.write( "   52C13\r\n" );
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document.write( "The answer is 9.655370011×10-4 or about\r\n" );
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document.write( ".0009655370011\r\n" );
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document.write( "Edwin

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