document.write( "Question 831148: a,b,c,d and e went to a concert. They sit in 5 adjacent seats. How many arrangements are possible if:_
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Algebra.Com's Answer #501933 by Edwin McCravy(20055) $\"\"$ $\"About$

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a) a insists on sitting with b.
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document.write( "That's the number of arrangements of \r\n" );
document.write( "the four things {ab, c, d, e}, which is 4! or 24. \r\n" );
document.write( "PLUS\r\n" );
document.write( "the number of arrangements of \r\n" );
document.write( "the four things {ba, c, d, e}, which is also 4! or 24.\r\n" );
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document.write( "Answer = 2×24 = 48 ways.\r\n" );
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\n" ); document.write( "b) c refuses to sit with d.
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document.write( "First we find the number of ways anybody can sit anywhere.\r\n" );
document.write( "That's the number of arrangements of \r\n" );
document.write( "the four things {a, b, c, d, e}, which is 5! or 120.\r\n" );
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document.write( "The we subtract from that 5! the number of unwanted arrangements.\r\n" );
document.write( "The unwanted arrangements are \r\n" );
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document.write( "The number of arrangements of \r\n" );
document.write( "the four things {a, b, cd, e}, which is 4! or 24. \r\n" );
document.write( "PLUS\r\n" );
document.write( "he number of arrangements of \r\n" );
document.write( "the four things {a, b, dc, e}, which is also 4! or 24.\r\n" );
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document.write( "as that's 2×24 just as in part a), \r\n" );
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document.write( "[so we could have just observed that the number of unwanted\r\n" );
document.write( "arrangements here was the same as the answer to a), 48]\r\n" );
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document.write( "Answer: 5! - 2×4! = 120 = 2×24 = 120 - 48 = 72\r\n" );
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document.write( "Edwin

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