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document.write( "For some reason, when problems are about sitting around a table,\r\n" );
document.write( "all the rotations as shown below are considered the same. (I don't \r\n" );
document.write( "believe they should be the same, but mathematicians do consider them\r\n" );
document.write( "the same seating arrangement, so I will here. You might want to ask\r\n" );
document.write( "your teacher about whether that should be the case.)\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "I am assuming that all 7 of those above are considered as the\r\n" );
document.write( "same seating arrangement.\r\n" );
document.write( "\r\n" );
document.write( "If it doesn't matter where Jack and Jill sit, the number of ways is 7!/7.\r\n" );
document.write( "(We divide by 7 because all the 7 seating arrangements\r\n" );
document.write( "pictured above are considered the same. And 7!/7 is just 6!.\r\n" );
document.write( "\r\n" );
document.write( "Now we must calculate the number of ways Jack and Jill sit together.\r\n" );
document.write( "Imagine there being only 6 chairs and Jill sits in Jack's lap. That's \r\n" );
document.write( "the same as when Jack is seated left of Jill. That's 6!/6 or 5! ways.\r\n" );
document.write( "But there is another, by imagining only 6 chairs with Jack sitting in \r\n" );
document.write( "Jill's lap. That's the same as when Jack is seated right of Jill. \r\n" );
document.write( "That's another 6!/6 or 5! ways. So there are 2*5! ways they sit together. \r\n" );
document.write( "\r\n" );
document.write( "P(they sit together) = 2*5!/6! = 2*(5*4*3*2*1)/(6*5*4*3*2*1) = 2/6 = 1/3\r\n" );
document.write( "\r\n" );
document.write( "Therefore P(they do not sit together) = 1 = 1/3 = 2/3.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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document.write( "![\"\"](\"/images/stars/stars-12.gif\")
