document.write( "Question 1141007: How many ways can 7 people be seated in a row of chairs if two of the people, Wilma and Paul, refuse to sit each other? \n" ); document.write( "

Algebra.Com's Answer #761553 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "The number of all possible \"in line\" arrangements for 7 people is \r\n" );
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document.write( "    7! = 1*2*3*4*5*6*7 = 5040\r\n" );
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document.write( "if NO RESTRICTIONS are imposed.\r\n" );
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document.write( "The number of all possible arrangements where Wilma and Paul are neighbors is\r\n" );
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document.write( "    2*6! = 2*(1*2*3*4*5*6) = 2*720 = 1440.\r\n" );
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document.write( "(The factor \"2\" in this formula reflects two possible arrangements of Wilma and Paul as neighbors.)\r\n" );
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document.write( "The number which is the answer to the problem's question is the difference\r\n" );
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document.write( "    7! - 2*6! = 5040 - 1440 = 3600.    ANSWER\r\n" );
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