document.write( "Question 990529: Find the number of ways in which a committee, its chairman and its president can be
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document.write( "selected from a set of n people. A person can be chairman as well as president. Committee
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document.write( "can have any number of people?
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Algebra.Com's Answer #610822 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "Choose the chairman any of n ways.\r\n" ); document.write( "Choose the president any of n ways. \r\n" ); document.write( "That's nē ways to choose the chairman and president.\r\n" ); document.write( "For each of the remaining n-2 people, we can make two choices, either\r\n" ); document.write( "\r\n" ); document.write( "1. to choose him/her to serve on the committee, or \r\n" ); document.write( "2. to choose him/her not to serve on the committee.\r\n" ); document.write( "\r\n" ); document.write( "That's 2n-2, counting the cases where only the chairman and\r\n" ); document.write( "president make up a 2-member committee.\r\n" ); document.write( "\r\n" ); document.write( "Answer: n2*2n-2, assuming it is possible to choose\r\n" ); document.write( "nobody else but the chairman and president. Otherwise the answer is\r\n" ); document.write( "n2*(2n-2-1), where we must have at least one other person. You'll have \r\n" ); document.write( "to ask your teacher whether or not 2-member committees are to be counted.\r\n" ); document.write( "\r\n" ); document.write( "Edwin \n" ); document.write( " \n" ); document.write( " |