document.write( "Question 1175241: Vanessa plans to arrange A, B, C, D, E, F, G, and H in a row on the wall. Find
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\n" ); document.write( "1. A and B must be placed next to each other.
\n" ); document.write( "2. A and B must not be placed next to each other.
\n" ); document.write( "3. A, B, and C must be placed next to each other, and at the same time, E,F and G must also be placed next to each other. \n" ); document.write( "
Algebra.Com's Answer #800829 by Edwin McCravy(20056)\"\" \"About 
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Vanessa plans to arrange A, B, C, D, E, F, G, and H in a row on the wall. Find
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\n" ); document.write( "1. A and B must be placed next to each other.
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document.write( "Case I:  A is immediately left of B\r\n" );
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document.write( "Then she has only 7 things to arrange:  AB, C, D, E, F, G, H\r\n" );
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document.write( "That's 7! ways.\r\n" );
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document.write( "Case II:  A is immediately right of B\r\n" );
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document.write( "Then she has only 7 things to arrange:  BA, C, D, E, F, G, H\r\n" );
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document.write( "That's also 7! ways.\r\n" );
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document.write( "Answer: 7!+7! = 2*7! = 2*5040 = 10080
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\n" ); document.write( "2. A and B must not be placed next to each other.
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document.write( "We calculate the number of ways the 8 things can be arranged without\r\n" );
document.write( "restriction, and then subtract the result of problem 1:\r\n" );
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document.write( "8!-2*7! = 40320-10080 = 30240 \r\n" );
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3. A, B, and C must be placed next to each other, and at the same time,
\n" ); document.write( "E,F and G must also be placed next to each other.
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document.write( "A,B, and C can be placed together in 3! or 6 ways.\r\n" );
document.write( "E,F, and G can be placed together in 3! or 6 ways.\r\n" );
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document.write( "That's 6*6 or 36 ways to group A,B,C and E,F,G\r\n" );
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document.write( "For each of those 36 ways to arrange those two triplets, there are 4 things to\r\n" );
document.write( "arrange, {A,B,C}, (E,F,G}, D, and H.  That's 4!=24 ways.\r\n" );
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document.write( "Answer 6*6*24 = 864 ways.\r\n" );
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document.write( "Edwin
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