document.write( "Question 651332: twelve people are to travel by three different cars,each of which holds four.Find the number of ways in which the party may be divided if two people refuse to travel in the same car;
\n" ); document.write( "(1)Assume the antagonists travel in the same car;
\n" ); document.write( "(2)Solve by actually placing the two in different cars.
\n" ); document.write( " finally,compare your answers in (1)and (2).\r
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\n" ); document.write( "\n" ); document.write( "(PLEASE I REALLY NEED THE SOLUTION BEFORE NEXT SATURDAY BECAUSE I'LL BE GOING BACK TO SCHOOL.THANK YOU VERY VERY MUCH.) \n" ); document.write( "
Algebra.Com's Answer #407613 by Edwin McCravy(20056)\"\" \"About 
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twelve people are to travel by three different cars,each of which holds four.Find the number of ways in which the party may be divided if two people refuse to travel in the same car;
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\n" ); document.write( " (1)Assume the antagonists travel in the same car;
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document.write( "Let the cars be a Ford (car number 1), a Chevy (car number 2), and a \r\n" );
document.write( "Honda (car number 3)\r\n" );
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document.write( "Let the antagonists be John and Henry.\r\n" );
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document.write( "First find the number of ways anybody can ride in any car.\r\n" );
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document.write( "We can choose the four for the Ford in C(12,4) ways.\r\n" );
document.write( "We can choose the four for the Chevy in C(8,4) ways.\r\n" );
document.write( "We must choose the four for the Honda in C(4,4)=1 way.\r\n" );
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document.write( "That's C(12,4)·C(8,4)·C(4,4) = 495·70·1 = 34650\r\n" );
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document.write( "From that number we must subtract the number of ways John and\r\n" );
document.write( "Henry can ride in the same car.\r\n" );
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document.write( "We can choose the car they ride in in C(3,1)=3 ways.\r\n" );
document.write( "We can choose the other two people to ride with them in C(10,2) ways.\r\n" );
document.write( "We can choose the four people for the car with the smaller car number \r\n" );
document.write( "that they don't ride in in C(8,4) ways.\r\n" );
document.write( "We can choose the four for the car with the larger car number that \r\n" );
document.write( "they don't ride in in C(4,4)=1 way.\r\n" );
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document.write( "That's C(3,1)·C(10,2)·C(8,4)·C(4,4) = 3·45·70·1 = 9450\r\n" );
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document.write( "So the answer is 34650-9450 = 25200\r\n" );
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\n" ); document.write( "(2)Solve by actually placing the two in different cars.
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document.write( "We can choose the car for John to ride in in C(3,1)=3 ways.\r\n" );
document.write( "We can choose the car for Henry to ride in in C(2,1)=2 ways.\r\n" );
document.write( "We can choose the 3 people to ride with John in C(10,3) ways.\r\n" );
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document.write( "[Notice at this point we have 4 people seated in the car that \r\n" );
document.write( "has John in it and Henry is sitting alone in another car.  So\r\n" );
document.write( "we have 5 people seated so far. That leaves 12-5 or 7 people \r\n" );
document.write( "left to seat.] \r\n" );
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document.write( "We can choose the 3 people to ride with Henry in C(7,3) ways.\r\n" );
document.write( "We can choose the 4 remining people to ride in the remaining car\r\n" );
document.write( "in C(4,4)=1 way.\r\n" );
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document.write( "That's C(3,1)·C(2,1)·C(10,3)·C(7,3)·C(4,4) = 3·2·120·35·1 = 25200\r\n" );
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\n" ); document.write( "finally,compare your answers in (1)and (2).
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document.write( "They are exactly the same, both being 25200 ways.\r\n" );
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document.write( "Edwin
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