document.write( "Question 881366: A student club consists of 8 guys and 12 girls. A committee of 8 is to be selected. In how many ways can this be done if
\n" ); document.write( " the committee must have the same number of guys as girls\r
\n" ); document.write( "\n" ); document.write( "the committee must have at least 6 boys on it \r
\n" ); document.write( "\n" ); document.write( " three officers (president, vice president, secretary/treasurer) are selected from ALL the members.
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Algebra.Com's Answer #532265 by Edwin McCravy(20055) $\"\"$ $\"About$

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A student club consists of 8 guys and 12 girls. A committee of 8 is to be selected. In how many ways can this be done if
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document.write( "Order doesn't matter, so we use combinations:\r\n" );
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document.write( "Choose the 4 guys 8C4 ways and the 4 girls 12C4 ways.\r\n" );
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document.write( "Answer: (8C4)(12C4) = (70)(495) = 34560\r\n" );
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\n" ); document.write( "the committee must have at least 6 guys on it
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document.write( "Case 1:  6 guys and 2 girls.\r\n" );
document.write( "Choose the 6 guys 8C6 ways and the 2 girls 12C4 ways.\r\n" );
document.write( "Total for case 1: (8C6)(12C2) = (28)(66) = 1848.\r\n" );
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document.write( "Case 2:  7 guys and 1 girl.\r\n" );
document.write( "Choose the 7 guys 8C7 ways and the 1 girls 12C1 ways.\r\n" );
document.write( "Total for case 3: (8C7)(12C1) = (8)(12) = 96.\r\n" );
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document.write( "Case 3:  8 guys and no girls.\r\n" );
document.write( "Choose the 8 guys 8C8 ways.\r\n" );
document.write( "Total for case 3: (8C8)(12C2) = 1.\r\n" );
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document.write( "Total for all three cases = 1848+96+1 = 1945 ways.\r\n" );
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\n" ); document.write( "three officers (president, vice president, secretary/treasurer) are selected from ALL the members.
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document.write( "Here order matters, so we use permutations:  20P3 = 6840 ways.\r\n" );
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document.write( "Or you can think of it this way:\r\n" );
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document.write( "Choose the president any of 20 ways.\r\n" );
document.write( "Choose the vice president any of the remaining 19 ways.\r\n" );
document.write( "Choose the vice secretary/treasurer any of the remaining 18 ways.\r\n" );
document.write( "Answer: 20*19*18 = 6840\r\n" );
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document.write( "Edwin

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