If \(C_0, C_1, C_2, ..., C_{10}\) represent the binomial coefficients in the expansion of \((1+x)^{10}\), then \(C_0C_6 + C_1C_7 + C_2C_8 + C_3C_9 + C_4C_{10} = \)
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The sum \(\sum C_r C_k\) often relates to the coefficient of a term in the product of two binomial expansions. Using the identity \(^nC_r = ^nC_{n-r}\) is key to transforming the sum into a recognizable form, typically the coefficient of \(x^k\) in \((1+x)^{2n}\), which is \(^{2n}C_k\).