document.write( "Question 155008: hey could you please help me out with this permutation problem:\r
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Algebra.Com's Answer #114455 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\"P%28n%2C5%29=20P%28n%2C3%29\"
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document.write( "\"P%28n%2Cr%29=n%28n-1%29%28n-2%29\"···\"%28until_there_are_r_factors%29\"\r\n" );
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document.write( "So, \"P%28n%2C5%29=n%28n-1%29%28n-2%29%28n-3%29%28n-4%29\"\r\n" );
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document.write( "and \"P%28n%2C3%29=n%28n-1%29%28n-2%29\"\r\n" );
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document.write( "Substituting,\r\n" );
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document.write( "\"n%28n-1%29%28n-2%29%28n-3%29%28n-4%29=20%2An%28n-1%29%28n-2%29\"\r\n" );
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document.write( "Get a 0 on the right:\r\n" );
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document.write( "\"n%28n-1%29%28n-2%29%28n-3%29%28n-4%29-20%2An%28n-1%29%28n-2%29=0\"\r\n" );
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document.write( "factor out \"n%28n-1%29%28n-2%29\"\r\n" );
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document.write( "\"n%28n-1%29%28n-2%29%2A%28%28n-3%29%28n-4%29-20%29=0\"\r\n" );
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document.write( "Simplify the last parentheses:\r\n" );
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document.write( "\"n%28n-1%29%28n-2%29%28%28n%5E2-7n%2B12%29-20%29=0\"\r\n" );
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document.write( "\"n%28n-1%29%28n-2%29%28n%5E2-7n%2B12-20%29=0\"\r\n" );
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document.write( "\"n%28n-1%29%28n-2%29%28n%5E2-7n-8%29=0\"\r\n" );
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document.write( "Factor the last parentheses:\r\n" );
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document.write( "\"n%28n-1%29%28n-2%29%28n-8%29%28n%2B1%29=0\"\r\n" );
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document.write( "Setting each factor = 0, we get the\r\n" );
document.write( "solutions:\r\n" );
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document.write( "\"n=0\", \"n=1\", \"n=2\", \"n=8\", \"n=-1\".\r\n" );
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document.write( "The first three are considered correct,\r\n" );
document.write( "because when \"r+%3E+n\", \"P%28n%2Cr%29+=+0\"\r\n" );
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document.write( "And \"n=8\" is a solution.  But the last one\r\n" );
document.write( "\"n=-1\" is not a solution because permutations\r\n" );
document.write( "are not defined for negative numbers.\r\n" );
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document.write( "So the four solutions are\r\n" );
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document.write( "\"n=0\", \"n=1\", \"n=2\", \"n=8\"\r\n" );
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document.write( "Possibly your teacher may want only\r\n" );
document.write( "the solution \"n=8\"; however, the first \r\n" );
document.write( "three are solutions since they cause \r\n" );
document.write( "both sides of the original equation\r\n" );
document.write( "to equal 0.\r\n" );
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document.write( "Edwin
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