document.write( "Question 460272: how many was can 6 people be seated in a row if 3 of them insist on NOT sitting together? \n" ); document.write( "
Algebra.Com's Answer #315697 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I can't tell whether you mean that it is OK if two\r\n" );
document.write( "of them sit together as long as the third one isn't\r\n" );
document.write( "next to either of them, or whether you mean that no \r\n" );
document.write( "two of the three can sit together.\r\n" );
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document.write( "I will assume that it is OK if just two of them sit\r\n" );
document.write( "together, but not all three.\r\n" );
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document.write( "There are 6! or 720 ways any of the 6 can sit anywhere.\r\n" );
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document.write( "Now we must subtract all the ways in which the three\r\n" );
document.write( "sit together.  \r\n" );
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document.write( "There are 3! was they can sit in three adjacent seats.\r\n" );
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document.write( "When they sit together it is the same as seating 4 things\r\n" );
document.write( "in order, because the three boys together is like a single\r\n" );
document.write( "thing. So we must subtract 3!*4! from the 6!. So the answer is \r\n" );
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document.write( "6! - 3!*4! = 720 = 6*24 = 720 - 144 = 576\r\n" );
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document.write( "It's a more complicated problem if no two of the three can\r\n" );
document.write( "sit together.  The answer to that one is 144.  I won't show you\r\n" );
document.write( "that one unless that was what you meant.\r\n" );
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document.write( "Edwin

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