document.write( "Question 944709: From a group of six persons, how many committees of three can be formed if two of the six people cannot be on the same committee? \n" ); document.write( "

Algebra.Com's Answer #576774 by Edwin McCravy(20054) $\"\"$ $\"About$

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From a group of six persons, how many committees of three can be formed if two of the six people cannot be on the same committee?
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document.write( "1. First we do the problem allowing them to serve on the same committee.\r\n" );
document.write( "2. Then we do a second problem requiring them to serve on the same committee.\r\n" );
document.write( "3. Then we subtract the answer to (2) from the answer to (1).\r\n" );
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document.write( "1. That's 6 people choose 3 or 6C3 = 20\r\n" );
document.write( "2. If those two are on the same committee, we choose the a third man\r\n" );
document.write( "to serve with them.  There are 4 other men, so we can be on the same\r\n" );
document.write( "committee 4 ways. That's 4 people choose 1 or 4C1 or 4 ways.\r\n" );
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document.write( "3. Answer:  20-4 = 16 ways. \r\n" );
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document.write( "Checking:\r\n" );
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document.write( "Suppose the 6 people are Alan, Betty, Cathy, Donald, Edwin, and Flo.\r\n" );
document.write( "Suppose Alan and Betty will not serve on the same committee. \r\n" );
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document.write( "Here are all 16 committees. Notice that Alan and Betty are not \r\n" );
document.write( "together on any of them:\r\n" );
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document.write( " 1.  {Alan, Cathy, Donald}\r\n" );
document.write( " 2.  {Alan, Cathy, Edwin}\r\n" );
document.write( " 3.  {Alan, Cathy, Flo}\r\n" );
document.write( " 4.  {Alan, Donald, Edwin}\r\n" );
document.write( " 5.  {Alan, Donald, Flo}\r\n" );
document.write( " 6.  {Alan, Edwin, Flo}\r\n" );
document.write( " 7.  {Betty, Cathy, Donald}\r\n" );
document.write( " 8.  {Betty, Cathy, Edwin}\r\n" );
document.write( " 9.  {Betty, Cathy, Flo}\r\n" );
document.write( "10.  {Betty, Donald, Edwin}\r\n" );
document.write( "11.  {Betty, Donald, Flo}\r\n" );
document.write( "12.  {Betty, Edwin, Flo}\r\n" );
document.write( "13.  {Cathy, Donald, Edwin}\r\n" );
document.write( "14.  {Cathy, Donald, Flo}\r\n" );
document.write( "15.  {Cathy, Edwin, Flo}\r\n" );
document.write( "16.  {Donald, Edwin, Flo}\r\n" );
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document.write( "Edwin

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