document.write( "Question 964061: We have 20 women and 15 men.
\n" ); document.write( "We want to form a delegation of 5 people.
\n" ); document.write( "That delegation has to have 3 women.
\n" ); document.write( "But Susy and Mary can't be together in the delegation. \n" ); document.write( "
Algebra.Com's Answer #589046 by Edwin McCravy(20077)\"\" \"About 
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We have 20 women and 15 men.
\n" ); document.write( "We want to form a delegation of 5 people.
\n" ); document.write( "That delegation has to have 3 women.
\n" ); document.write( "But Susy and Mary can't be together in the delegation.
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document.write( "We have a difficulty with the third sentence.\r\n" );
document.write( "The statement \"That delegation has to have 3 woman\" can be taken\r\n" );
document.write( "two ways.\r\n" );
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document.write( "1. that there must be EXACTLY 3 women and therefore EXACTLY 2 men. \r\n" );
document.write( "2. that there msut be AT LEAST 3 women, (i.e., there can be 3 women,\r\n" );
document.write( "   4 women or all 5 women).\r\n" );
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document.write( "I will assume it is the first way, that there must be EXACTLY 3 women \r\n" );
document.write( "and EXACTLY 2 men. If it's the second way, let me know in the thank-\r\n" );
document.write( "you note form below, and I'll solve it that way.\r\n" );
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document.write( "First we solve the problem without regard to whether Susy and Mary can \r\n" );
document.write( "be together or not.\r\n" );
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document.write( "Choose the 3 women 20C3 = 1140 ways\r\n" );
document.write( "Choose the 2 men 15C2 = 105 ways.\r\n" );
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document.write( "That's (1140)(105) = 119700 ways.\r\n" );
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document.write( "Now from that number we must subtract the number of ways Susy and Mary\r\n" );
document.write( "can be together.\r\n" );
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document.write( "Choose the other woman besides Susy and Mary in 20-2=18 ways.\r\n" );
document.write( "Choose the 2 men 15C2 = 105 ways.\r\n" );
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document.write( "That's (18)(105) = 1890 ways.\r\n" );
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document.write( "So we subtract those 1890 forbidden ways from the 119700.\r\n" );
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document.write( "Answer 119700-1890 = 117810\r\n" );
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document.write( "Edwin
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