document.write( "Question 1206612: 10 people want to sit in a row with only 3 seats. What is the probability that a couple is not seated next to each other? \n" ); document.write( "
Algebra.Com's Answer #844183 by Edwin McCravy(20063)\"\" \"About 
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10 people want to sit in a row with only 3 seats.
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document.write( "Obviously they can't, so only 3 will be assigned to the 3 seats, and the other 7\r\n" );
document.write( "will be left standing. There is a particular couple among the 10 people, say,\r\n" );
document.write( "Alice and Ben. You want to know the probability that we have one of these\r\n" );
document.write( "seating arrangements\r\n" );
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document.write( "CXY, XCY, XYC, CXC, XYZ\r\n" );
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document.write( "where C represents either Alice or Ben, and where X, Y, Z are neither Alice\r\n" );
document.write( "nor Ben.\r\n" );
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document.write( "Each of the 1st 3 seating arrangements can be chosen (2)(8)(7)=112 ways,\r\n" );
document.write( "so they account for (3)(112)=336 ways.\r\n" );
document.write( "The 4th case can be chosen (2)(8)(1)=16 ways.\r\n" );
document.write( "The 5th case can be chosen (8)(7)(6)=336 ways.\r\n" );
document.write( "That's 336+16+336=688 cases\r\n" );
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document.write( "The total ways any 3 of the 10 can be seated. Choose the 3 to be seated in\r\n" );
document.write( "(10)(9)(8)=720\r\n" );
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document.write( "Desired probability = 688/720 = 43/45\r\n" );
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document.write( "I just realized it would be easier to go for the complement event.\r\n" );
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document.write( "CCX, XCC.\r\n" );
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document.write( "Choose the CC 2 ways and X 8 ways. That's 16 ways for CCX and 16 ways for XCC.\r\n" );
document.write( "So there are (2)(16)=32 unsuccessful ways out of (10)(9)(8)=720 ways, leaving\r\n" );
document.write( "688 successful ways, out of 720.\r\n" );
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document.write( "Answer: 688/720 = 43/45.\r\n" );
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document.write( "Edwin
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