document.write( "Question 38562: The 8 people at a party shook hands exactly once with each of the others before the 9th arrived. The 9th person then shook hands with some of these 8 people. A
\n" ); document.write( "total of 32 handshakes took place. With how many people did the 9th person shake hands? \n" ); document.write( "
Algebra.Com's Answer #24080 by AnlytcPhil(1807)\"\" \"About 
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The 8 people at a party shook hands exactly once with each of the others before\r\n" );
document.write( "the 9th arrived. The 9th person then shook hands with some of these 8 people. A \r\n" );
document.write( "total of 32 handshakes took place. With  how many people did the 9th person\r\n" );
document.write( "shake hands?\r\n" );
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document.write( "Before the 9th person arrived there were \"combinations of 8 things taken 2 at a\r\n" );
document.write( "time\".  It is combinations, not permutations, because the order in which they\r\n" );
document.write( "stand to shake hands does not matter.\r\n" );
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document.write( "C(8,2) = 8!/(2!6!) = 28 handshakes before the 9th person arrived\r\n" );
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document.write( "After the 9th person finished shaking hands, there were 32 handshakes\r\n" );
document.write( "altogether.\r\n" );
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document.write( "Therefore the 9th person shook hands with 32 - 28 or 4 people.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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