document.write( "Question 933503: Ten women and ten men are on the faculty in the mathematics department
\n" ); document.write( "at a school.
\n" ); document.write( "
\n" ); document.write( "- How many ways are there to select a committee of five members of the
\n" ); document.write( "department if at least one woman must be on the committee?
\n" ); document.write( "- How many ways are there to select a committee of five members of the
\n" ); document.write( "department if at least one woman and at least one man must be on the committee? \n" ); document.write( "

Algebra.Com's Answer #567934 by AnlytcPhil(1806) $\"\"$ $\"About$

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Ten women and ten men are on the faculty in the mathematics department
\n" ); document.write( "at a school.
\n" ); document.write( "
\n" ); document.write( "- How many ways are there to select a committee of five members of the
\n" ); document.write( "department if at least one woman must be on the committee?
\n" ); document.write( "

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document.write( "1. We find the number of ways to select any 5 people, regardless of gender.\r\n" );
document.write( "2. We find the number of ways to select 5 men.\r\n" );
document.write( "3. We subtract the result of 2 from the result of 1.\r\n" );
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document.write( "1. That's C(20,5)\r\n" );
document.write( "2. That's C(10,5)\r\n" );
document.write( "3. That's C(20,5)-C(10,5) = 15504-252 = 15252 \r\n" );
document.write( "

\n" ); document.write( "- How many ways are there to select a committee of five members of the
\n" ); document.write( "department if at least one woman and at least one man must be on the committee?
\n" ); document.write( "

 \r\n" );
document.write( "1. We find the number of ways to select any 5 people, regardless of gender.\r\n" );
document.write( "2. We find the number of ways to select 5 men.\r\n" );
document.write( "3. We find the number of ways to select 5 women.\r\n" );
document.write( "4. We subtract the result of 2 and the result of 3 from the result of 1.\r\n" );
document.write( "\r\n" );
document.write( "1. That's C(20,5)\r\n" );
document.write( "2. That's C(10,5)\r\n" );
document.write( "3. That's C(10,5)\r\n" );
document.write( "4. That's C(20,5)-C(10,5)-C(10,5) = 15504-252-252 = 15000.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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