document.write( "Question 536053: A class has 7 students. Two of the students, Rachel and Jonathan cannot stop bugging each other. How many line-ups are possible in which Jonathan and Rachel are not beside each other? \n" ); document.write( "
Algebra.Com's Answer #352110 by Edwin McCravy(20055)\"\" \"About 
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document.write( "Suppose the set of students is {A,B,C,D,E,R,J}, where R is Rachel and J is Jonathan.\r\n" );
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document.write( "First calculate how many ways there are to arrange the seven \"things\",\r\n" );
document.write( "{A,B,C,D,E,R,J}, whether R and J are together or not:\r\n" );
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document.write( "That is 7! or 5040\r\n" );
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document.write( "Now we must subtract from that all the ways R and J are together.\r\n" );
document.write( "These consist of: \r\n" );
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document.write( "(A)   the number of ways to arrange the 6 \"things of the set {A,B,C,D,E,(RJ)},\r\n" );
document.write( "with (RJ) considered as a SINGLE \"thing\", where R is on the left of J:\r\n" );
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document.write( "That is 6! or 720\r\n" );
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document.write( "(B)  the number of ways to arrange the 6 \"things of the set {A,B,C,D,E,(JR)},\r\n" );
document.write( "with (JR) considered as a SINGLE \"thing\", where J on the left of R:\r\n" );
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document.write( "That is also 6! or 720\r\n" );
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document.write( "So the final answer is \r\n" );
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document.write( "7! - 6! - 6! = 7! - 2·6! = 5040 - 2(720) = 5040 - 1440 = 3600\r\n" );
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document.write( "Edwin
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