document.write( "Question 1205092: #1.
\n" ); document.write( "Prove for all integers n, k, and r with n ≥ k ≥ r that nCk×kCr = nCr×(n-r)C(k-r)\r
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\n" ); document.write( "The binomial theorem states that for any real numbers a and b,
\n" ); document.write( "(a + b)n =∑_(k=0)^n▒〖(n¦k) a^(n-k) b^k 〗 for any integer n ≥ 0.
\n" ); document.write( "Use this theorem to show that for any integer n ≥ 0, ∑_(k=0)^n▒〖〖(-1)〗^k (n¦k) 3^(n-k) 2^k 〗 = 1.\r
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Algebra.Com's Answer #841731 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%28nCk%29%28kCr%29+=+%28nCr%29%28n-r%29C%28k-r%29\"\r\n" );
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document.write( "\"%28n%21%2F%28k%21%28n-k%29%21%29%29%2A%28k%21%2F%28r%21%28k-r%29%21%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"%22%22=%22%22\"\r\n" );
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document.write( "\"n%21%2F%28%28n-k%29%21r%21%28k-r%29%21%29\"\"%22%22=%22%22\"\"n%21%2F%28r%21%28k-r%29%21%28n-k%29%21%29%29\"\r\n" );
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document.write( "Those are the same except for the order of factors in the denominator.\r\n" );
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document.write( "Your notation in the second one is incompatible with this site, making it\r\n" );
document.write( "so garbled, I can't make it out.\r\n" );
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document.write( "Edwin
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