document.write( "Question 266416: find the number of permutations of letters of CALENDAR in which C and A are together but N and D are not? \n" ); document.write( "
Algebra.Com's Answer #195753 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
find the number of permutations of letters of CALENDAR in which C and A are together but N and D are not?
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document.write( "That's \r\n" );
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document.write( "the number of ways C&A are together \r\n" );
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document.write( "minus\r\n" );
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document.write( "the number or ways C&A are together and N&D are together\r\n" );
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document.write( "So:\r\n" );
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document.write( "N(C&A together) =  number of permutations of these 7 things:\r\n" );
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document.write( "{CA,L,E,N,D,A,R), which is 7! \r\n" );
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document.write( "plus the number of permutations of these 7 things:\r\n" );
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document.write( "{AC,L,E,N,D,A,R), which is also 7!\r\n" );
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document.write( "So that's 2*7!\r\n" );
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document.write( "N(C&A together and N&D together) = \r\n" );
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document.write( "the number of permutations of these 6 things:\r\n" );
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document.write( "{CA,L,E,ND,A,R} which is 6!\r\n" );
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document.write( "plus \r\n" );
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document.write( "the number of permutations of these 6 things:\r\n" );
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document.write( "{CA,L,E,DN,A,R} which is 6!\r\n" );
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document.write( "plus\r\n" );
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document.write( "the number of permutations of these 6 things:\r\n" );
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document.write( "{AC,L,E,ND,A,R} which is 6!\r\n" );
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document.write( "plus\r\n" );
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document.write( "the number of permutations of these 6 things:\r\n" );
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document.write( "{AC,L,E,DN,A,R} which is 6!\r\n" );
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document.write( "which is 4*6!\r\n" );
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document.write( "Therefore the desired number is \r\n" );
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document.write( "2*7! - 4*6! = 2*5040 - 4*720 = 10080 - 2880 = 7200 \r\n" );
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document.write( "Edwin
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