document.write( "Question 972621: You want to form a committee of 3 girls and 2 boys from a group of 8 girls and 6 boys. John is one of the boys, and Marie is one of the girls. How many committees are possible if John and Marie cannot be on the committee together? \n" ); document.write( "

Algebra.Com's Answer #595421 by Edwin McCravy(20055) $\"\"$ $\"About$

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You want to form a committee of 3 girls and 2 boys from a group of 8 girls and 6
\n" ); document.write( "boys. John is one of the boys, and Marie is one of the girls. How many
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document.write( "1. First we do the problem just as though it didn't matter whether John and\r\n" );
document.write( "Marie were on the committee together or not.  \r\n" );
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document.write( "2. Then we'll calculate the number of ways John and Marie could be on the\r\n" );
document.write( "committee together.\r\n" );
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document.write( "3.  Then we'll subtract the result of 2 from the result of 1.\r\n" );
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document.write( "1. \r\n" );
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document.write( "We choose the 3 girls:\r\n" );
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document.write( "That's \"8 girls Choose 3\" = 8 Choose 3 = 8C3 = \r\n" );
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document.write( "For each of those 56 ways we can choose the 3 girls, we choose the 2 boys:\r\n" );
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document.write( "That's \"6 boys Choose 2\" = 6 Choose 2 = 6C2 = \r\n" );
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document.write( "So the number of committees with no regard to whether or not John and Marie are\r\n" );
document.write( "together is (56)(15) = 840 ways  \r\n" );
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document.write( "2.\r\n" );
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document.write( "We choose John and Marie to be together on the committee in 1 way.  \r\n" );
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document.write( "We choose the other 2 girls from the 7 girls besides Marie:\r\n" );
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document.write( "That's \"7 boys Choose 2\" = 7 Choose 2 = 6C2 = \r\n" );
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document.write( "  \r\n" );
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document.write( "For each of those 21 ways to choose the other 2 girls, we can choose the 1 other\r\n" );
document.write( "boy from the other 5 boys besides John.\r\n" );
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document.write( "That's 5 boys choose 1 = 5C1 =  = 5\r\n" );
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document.write( "So the number of committees with John and Marie together is (1)(21)(5) = 105\r\n" );
document.write( "ways.\r\n" );
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document.write( "3. Subtracting the result of 2 from the result of 1:\r\n" );
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document.write( "840 - 105 = 735 ways.\r\n" );
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document.write( "Edwin

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