document.write( "Question 968384: If you were to draw a 5-card hand from a standard deck of 52 cards, what is the probability that it will have 3 face cards (from the 4 jacks, 4 queens, and 4 kings)? \n" ); document.write( "

Algebra.Com's Answer #591770 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "It is not clear whether the words \"it will have 3 face cards\" means \r\n" );
document.write( "\"EXACTLY 3 and no more\" or whether it means \"AT LEAST 3\".\r\n" );
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document.write( "I will considering that it means getting EXACTLY 3 face cards and no more.\r\n" );
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document.write( "The denominator of the desired probability in either case is\r\n" );
document.write( "the number of ways to choose 5 cards from the 52: \r\n" );
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document.write( "52 Choose 5 = 52C5 = \r\n" );
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document.write( "After cancelling and multiplying or multiplying and dividing, we get 2598960\r\n" );
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document.write( "The numerator of the desired probability in this case is\r\n" );
document.write( "the number of ways to choose 3 cards from the 12 face cards and\r\n" );
document.write( "2 cards from the other 40 non-face cards \r\n" );
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document.write( "12 Choose 3 = 12C3 = \r\n" );
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document.write( "After cancelling and multiplying or multiplying and dividing, we get 220\r\n" );
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document.write( "For each of those ways to get exactly 3 face cards, there are 40C2 ways\r\n" );
document.write( "to choose 2 non-face cards to go with the 3 face cards.\r\n" );
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document.write( "40 Choose 2 = 40C2 = \r\n" );
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document.write( "After cancelling and multiplying or multiplying and dividing, we get \r\n" );
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document.write( "So the number of possible hands with EXACTLY 3 face cards and EXACTLY 2 non-face cards is 220*780 = 171600\r\n" );
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document.write( "So the probability of getting EXACTLY 3 face cards and EXACTLY 2 non-face cards is\r\n" );
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document.write( " which reduces to  or about 6.6% of the time.\r\n" );
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document.write( "---------------------------\r\n" );
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document.write( "If your problem means \"AT LEAST 3 face card\", then we have to find the\r\n" );
document.write( "probability of getting EXACTLY 4 face cards and EXACTLY 1 non-face card.\r\n" );
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document.write( "AND\r\n" );
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document.write( "the probability of getting ALL 5 face cards.\r\n" );
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document.write( "and add those two probabilities to the \r\n" );
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document.write( "These will be found similar to the other case.\r\n" );
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document.write( "Edwin

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