document.write( "Question 927195: There are 6 boys and 18 girls in a class. A group of 5 students is needed to work on a project. If at least 2 boys are needed, how many different groups of 5 students are possible? \n" ); document.write( "

Algebra.Com's Answer #563177 by Edwin McCravy(20055) $\"\"$ $\"About$

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There are 6 boys and 18 girls in a class. A group of 5 students is needed to work on a project.
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document.write( "Strategy:  First find the number of groups of 5 students without regard to\r\n" );
document.write( "whether the group contains at least 2 boys or not. Then we will calculate\r\n" );
document.write( "the number of groups to eliminate which contain either no boys (all girls) \r\n" );
document.write( "or only one boy (4 girls and 1 boy).\r\n" );
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document.write( "1.  The number of groups of 5 without regard to whether there are at least 2\r\n" );
document.write( "boys.  That's C(24,5) = 42504.\r\n" );
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document.write( "2.  The number of groups with no boys, (all girls) is C(18,5) = 8568, which\r\n" );
document.write( "    we must subtract.\r\n" );
document.write( "3.  The number of groups with only 1 boy and 4 girls. \r\n" );
document.write( "    Choose the boy 6 ways.\r\n" );
document.write( "    For each of those ways, we can choose the 4 girls C18,4) ways.\r\n" );
document.write( "    That's 6*C(18,4) = 6*3060 = 18360, which we must subtract. \r\n" );
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document.write( "So we subtract those:\r\n" );
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document.write( "Answer: 42504-8568-18360 = 15576.\r\n" );
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document.write( "Edwin

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