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Find the value of .^(20)C(0) xx .^(13)...

Find the value of
`.^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10)`.

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AI Generated Solution

To solve the problem, we need to evaluate the expression: \[ ^{20}C_{0} \cdot ^{13}C_{10} - ^{20}C_{1} \cdot ^{12}C_{9} + ^{20}C_{2} \cdot ^{11}C_{8} - \ldots + (-1)^{10} \cdot ^{20}C_{10} \] This expression can be interpreted using the Binomial Theorem. The coefficients in the expression can be derived from the expansion of the binomials. ...
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