document.write( "Question 117274: 7P(n,3) = 6P(n+1,3)
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Algebra.Com's Answer #85298 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "\"7P%28n%2C3%29\" = \"6P%28n%2B1%2C3%29\"\r\n" );
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document.write( "Not sure why the answer is n=20.\r\n" );
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document.write( "Use the identity \"P%28k%2Cr%29\" = \"k%21%2F%28%28k-r%29%21%29\"\r\n" );
document.write( "to rewrite the permutations on both sides:\r\n" );
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document.write( "\"7%28n%21%2F%28n-3%29%21%29++\" = \"+6%28%28n%2B1%29%21%2F%28n%2B1-3%29%21%29\"\r\n" );
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document.write( "\"%287n%21%29%2F%28n-3%29%21++\" = \"+%286%28n%2B1%29%21%29%2F%28n-2%29%21%29\"\r\n" );
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document.write( "Multiply both sides by \"%28n-2%29%21%2F1\"\r\n" );
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document.write( "\"%28n-2%29%21%2F1\"\"%287n%21%29%2F%28n-3%29%21++\" = \"%28n-2%29%21%2F1\"\"+%286%28n%2B1%29%21%29%2F%28n-2%29%21%29\"\r\n" );
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document.write( "On the left, write \"%28n-2%29%21\" as \"%28n-2%29%28n-3%29%21\"\r\n" );
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document.write( "\"%28%28n-2%29%28n-3%29%21%29%2F1\"\"%287n%21%29%2F%28n-3%29%21++\" = \"%28n-2%29%21%2F1\"\"+%286%28n%2B1%29%21%29%2F%28n-2%29%21%29\"\r\n" );
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document.write( "Cancel the \"%28n-3%29%21\"'s on the left and the\r\n" );
document.write( "\"%28n-2%29%21\"'s on the right:\r\n" );
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document.write( "\"%28n-2%29+++cross%28%28n-3%29%21%29++++%29%2F1\"\"%287n%21%29%2F%28cross%28++%28n-3%29%21%29%29++\" = \"cross%28%28n-2%29%21%29%29%2F1\"\"+%286%28n%2B1%29%21%29%2Fcross%28%28n-2%29%21%29%29%29\"\r\n" );
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document.write( "\"7%28n-2%29n%21\" = \"6%28n%2B1%29%21\"\r\n" );
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document.write( "On the right, write \"%28n%2B1%29%21\" as \"%28n%2B1%29n%21\"\r\n" );
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document.write( "\"7%28n-2%29n%21\" = \"6%28n%2B1%29n%21\"\r\n" );
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document.write( "Divide both sides by \"n%21\"\r\n" );
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document.write( "\"7%28n-2%29\" = \"6%28n%2B1%29\"\r\n" );
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document.write( "\"7n-14%29\" = \"6n%2B6%29\"\r\n" );
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document.write( "\"n\" = \"20\"\r\n" );
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document.write( "Edwin
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