document.write( "Question 936633: In how many ways can five students be seated in row of eight seat if a certain two students
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Algebra.Com's Answer #570162 by Edwin McCravy(20055)\"\" \"About 
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In how many ways can five students
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document.write( "Suppose the students are A,B,C,D and E\r\n" );
document.write( "and the seats are 1,2,3,4,5,6,7 and 8\r\n" );
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\n" ); document.write( "be seated in row of eight seat if a certain two students\r
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document.write( "Suppose A and B insist on sitting together.\r\n" );
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document.write( "Case 1:  A sits left of B\r\n" );
document.write( "There are 7 ways to choose their seats: 1&2,2&3,3&4,4&5,5&6,6&7, and 7&8\r\n" );
document.write( "That's 7 ways:\r\n" );
document.write( "Case 2:  A sits right of B\r\n" );
document.write( "That's also 7 ways.\r\n" );
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document.write( "That's 14 ways to place A and B together\r\n" );
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document.write( "There are now 6 seats left and 3 students C,D, and E left to seat.\r\n" );
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document.write( "For each of those 14 ways to seat A and B, there are\r\n" );
document.write( "6 ways to seat C.  That's 14*6 ways to seat A,B and C.\r\n" );
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document.write( "There are now 5 seats left and 2 students D and E left to seat.\r\n" );
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document.write( "For each of those 14*6 ways to seat A,B and C, there are\r\n" );
document.write( "5 ways to seat D.  That's 14*6*5 ways to seat A,B,C and D.\r\n" );
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document.write( "There are 4 seats left and 1 student, E, left to seat.\r\n" );
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document.write( "For each of those 14*6*5 ways to seat A,B,C and C, there are\r\n" );
document.write( "4 ways to seat D.  That's 14*6*5*4 ways to seat A,B,C,D and E.\r\n" );
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document.write( "Answer: 14*6*5*4 = 1680 ways.\r\n" );
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\n" ); document.write( "b) Refuse to sit next to each other
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document.write( "There are 8 ways to seat A, 7 ways to seat B, 6 ways to seat C,\r\n" );
document.write( "5 ways to seat D and 4 ways to seat E.\r\n" );
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document.write( "That's 8*7*6*5*4 = 6720 ways anybody can sit in any seat.\r\n" );
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document.write( "We subtract 1680 ways A and B sit together.\r\n" );
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document.write( "Answer 6720-1680 = 5040.\r\n" );
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document.write( "Edwin
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