document.write( "Question 1098474: Out of 11 biologists and 6 physicists, a committee consisting of 8 biologists and 2 physicists is to be formed. In how many ways can this be done if two particular biologist cannot be on the committee together? \n" ); document.write( "

Algebra.Com's Answer #713355 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
Out of 11 biologists and 6 physicists, a committee consisting of 8 biologists and 2 physicists is to be formed. In how many ways can this be done if two particular biologists cannot be on the committee together?\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "So there are 2 \"restricted\" biologists and 9 non-\"restricted\" biologists.\r\n" );
document.write( "\r\n" );
document.write( "So the committee consists of either:\r\n" );
document.write( "\r\n" );
document.write( "Case 1: 1 restricted biologist, 7 non-resticted biologists, and 2 physicists.  \r\n" );
document.write( "\r\n" );
document.write( "Choose the 1 restricted biologist in 2C1 ways.  (2 choose 1)\r\n" );
document.write( "Choose the 7 non-restricted biologists in 9C7 ways. (9 choose 7)\r\n" );
document.write( "Choose the 2 physicists in 6C2 ways. (6 choose 2)\r\n" );
document.write( "\r\n" );
document.write( "That's (2C1)(9C7)(6C2).\r\n" );
document.write( "\r\n" );
document.write( "          OR\r\n" );
document.write( "\r\n" );
document.write( "Case 2: 8 non-restricted biologists, and 2 physicists.  \r\n" );
document.write( "\r\n" );
document.write( "Choose the 8 non-restricted biologists in 9C8 ways. (9 choose 8)\r\n" );
document.write( "Choose the 2 physicists in 6C2 ways. (6 choose 2)\r\n" );
document.write( "\r\n" );
document.write( "That's (9C8)(6C2).\r\n" );
document.write( "\r\n" );
document.write( "Total for both cases:  (2C1)(9C7)(6C2) + (9C8)(6C2)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );