document.write( "Question 630948: Three friends board an airliner just before departure time. There are only 12 seats left, 4 of which are aisle seats. How many ways can the 3 people arrange themselves in available seats so that at least one of them sits on the aisle? \n" ); document.write( "

Algebra.Com's Answer #397239 by Edwin McCravy(20056) $\"\"$ $\"About$

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Three friends board an airliner just before departure time. There
\n" ); document.write( "are only 12 seats left, 4 of which are aisle seats. How many ways
\n" ); document.write( "can the 3 people arrange themselves in available seats so that at
\n" ); document.write( "least one of them sits on the aisle?
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document.write( "When you see the words \"at least one\", more than likely the problem \r\n" );
document.write( "is best solved by first finding the number of arrangements which \r\n" );
document.write( "either DO or DO NOT have the restriction.  Then we calculate the \r\n" );
document.write( "number of ways that DO NOT have the restriction and subtract that \r\n" );
document.write( "from the first number. That leaves the number that DO have the \r\n" );
document.write( "restriction.  The restriction here is that at least one of the three\r\n" );
document.write( "must sit in an aisle seat.\r\n" );
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document.write( "So first we calculate the number of ways the three can sit in any \r\n" );
document.write( "of the 12 seats, whether an aisle seat or not.\r\n" );
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document.write( "Suppose the three people are Tom, Dick, and Harry.  We can seat Tom \r\n" );
document.write( "in any of the 12 seats, Dick in any of remaining 11, and Harry in\r\n" );
document.write( "any of the remaining 10.  That's 12×11×10 ways to seat the three \r\n" );
document.write( "anywhere, aisle seats or not. \r\n" );
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document.write( "From that we must subtract the number of ways none of them sit in\r\n" );
document.write( "aisle seats.   \r\n" );
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document.write( "There are 4 aisle seats and therefore 12-4 or 8 non-aisle seats.\r\n" );
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document.write( "We can seat Tom in a non-aisle seat in any of 8 ways, Dick in any of\r\n" );
document.write( "the remaining 7 non-aisle seats, and Harry in any of the  remaining 6\r\n" );
document.write( "non-aisle seats. That's 8×7×6 ways to seat the three in non-aisle \r\n" );
document.write( "seats.\r\n" );
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document.write( "Now we subtract the 8×7×6 from the 12×11×10:\r\n" );
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document.write( "12×11×10 - 8×7×6 = 1320 - 336 = 984.\r\n" );
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document.write( "Edwin

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