document.write( "Question 750444: there are 14 girls and 10 boys in an algebra 2 class. what is the probability of a group of 4 having 3 girls and 1 boy \n" ); document.write( "

Algebra.Com's Answer #456663 by Edwin McCravy(20059) $\"\"$ $\"About$

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there are 14 girls and 10 boys in an algebra 2 class. what is the probability of a group of 4 having 3 girls and 1 boy
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document.write( "We calculate the numerator of the probability, which is the number of\r\n" );
document.write( "successful possibilities, of 3 girls and 1 boy.\r\n" );
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document.write( "The number of choices of 3 girls out of 14 girls, (14 choose 3), is C(14,3)\r\n" );
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document.write( "For every choice of 3 girls,\r\n" );
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document.write( "The number of choices of 1 boy out of 10 boys is (10 choose 1) or C(10,1)\r\n" );
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document.write( "So there are c(14,3)·C(10,1) choices of 3 girls and 1 boy.\r\n" );
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document.write( "We calculate the denominator of the probability, which is the number of\r\n" );
document.write( "all possibilites, successful or not, of any 4 people from the 14+10 or 24\r\n" );
document.write( "people.\r\n" );
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document.write( "That's the number of choices of 4 people out of 24 people, (24 choose 4), \r\n" );
document.write( "or C(14,3)\r\n" );
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document.write( "The desired probability is therefore\r\n" );
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document.write( "       C(14,3)C(10,1)     364·10     3640      260\r\n" );
document.write( "       —————————————— =  ———————— = ——————— = ————— ≈ 0.3425559947  \r\n" );
document.write( "           C(24,4)        10626      10626     759\r\n" );
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document.write( "Edwin

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