document.write( "Question 1162137: From a group of 6 girls and 7 boys, how many 5-member committees consist of
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Algebra.Com's Answer #785866 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "For this problem, remember that AND means to multiply and OR means to add.\r\n" );
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From a group of 6 girls and 7 boys, how many 5-member committees consist of
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document.write( "(6 girls CHOOSE 3) AND (7 boys CHOOSE 2) = (6C3)∙(7C2) = 20∙21 = 420 \r\n" );
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(b) 3 boys and 2 girls
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document.write( "(7 boys CHOOSE 3) AND (6 girls CHOOSE 2) = (7C3)∙(6C2) = 35∙15 = 525 \r\n" );
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(c) members of the same sex
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document.write( "(6 girls CHOOSE 5) OR (7 boys CHOOSE 5) = (6C5) + (7C5) = 6 + 21 = 26 \r\n" );
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(d) more boys than girls.
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document.write( "(6 girls CHOOSE 2) AND (7 boys CHOOSE 3) = (6C2)∙(7C2) = 15∙35 = 525\r\n" );
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document.write( "              OR\r\n" );
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document.write( "(6 girls CHOOSE 1) AND (7 boys CHOOSE 4) = (6C1)∙(7C4) = 6∙35 = 210 \r\n" );
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document.write( "              OR\r\n" );
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document.write( "7 boys CHOOSE 5 = 7C5 = 21  \r\n" );
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document.write( "Answer: 525 + 210 + 21 = 756\r\n" );
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One of the boys cannot get along with one of the girls. Find the
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document.write( "Number of committees that leave out the particular girl:\r\n" );
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document.write( "12 people CHOOSE 5 = 12C5 = 792\r\n" );
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document.write( "minus the number that leave out both the particular boy and girl:\r\n" );
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document.write( "11 people CHOOSE 5 = 11C5 = 462\r\n" );
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document.write( "That's 792-462 = 330\r\n" );
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document.write( "OR\r\n" );
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document.write( "Number of committees that leave out the particular boy:\r\n" );
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document.write( "12 people CHOOSE 5 = 12C5 = 792\r\n" );
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document.write( "minus the number that leave out both the particular boy and girl:\r\n" );
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document.write( "11 people CHOOSE 5 = 11C5 = 462\r\n" );
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document.write( "That's 792-462 = 330\r\n" );
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document.write( "Answer: 330 + 330 = 660\r\n" );
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document.write( "Edwin
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