document.write( "Question 1170989: Solve for n:\r
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Algebra.Com's Answer #795904 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hey, tutors, you two should be ashamed of yourselves! Leave this student alone!\r\n" );
document.write( "Those parentheses he or she had up there meant combinations, or if you prefer,\r\n" );
document.write( "binomial coefficients.  I rewrote it up there like he/she obviously meant it. \r\n" );
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document.write( "\"%28matrix%282%2C1%2CN%2CK%29%29\" means the same as C(N,K) or NCK. \r\n" );
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document.write( "The simplest way to evaluate combinations, or binomial coefficients, is not by\r\n" );
document.write( "using the definition, which is: \r\n" );
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document.write( "\"%28matrix%282%2C1%2CN%2CK%29%29=+N%21%2F%28K%21%28N-K%29%21%29\" \r\n" );
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document.write( "but by this:\r\n" );
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document.write( ", where there are the same number of factors in the numerator \r\n" );
document.write( "as in the factorial (K!) in the denominator.\r\n" );
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document.write( "So\r\n" );
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document.write( "Divide both sides by n:\r\n" );
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document.write( "\"matrix%281%2C3%2C%0D%0A%0D%0A12n-12%2C%0D%0A%22%22=%22%22%2C%0D%0An%5E2%2B3n%2B2%29%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C%0D%0A%0D%0A0%2C%0D%0A%22%22=%22%22%2C%0D%0An%5E2-9n%2B14%29%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C%0D%0A%0D%0A0%2C%0D%0A%22%22=%22%22%2C%0D%0A%28n-7%29%28n-2%29%29\"\r\n" );
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document.write( "n-7=0; n-2=0\r\n" );
document.write( "  n=7;   n=2\r\n" );
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document.write( "So there are two solutions.\r\n" );
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document.write( "They both check:\r\n" );
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document.write( "\"matrix%281%2C3%2C%0D%0A%0D%0A4%2A21%2C%0D%0A%22%22=%22%22%2C%0D%0A84%29%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C%0D%0A%0D%0A4%2A1%2C%0D%0A%22%22=%22%22%2C%0D%0A4%29%29\"\r\n" );
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document.write( "Edwin
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