Binomial fun

Consider the binomial expansion:

\[ (1+x)^n = C_0 + C_1 x + C_2 x^2+ C_3x^3 + \cdots + C_n x^n. \]

Find the value of \(C_{0}^{2} + C_{1}^{2} + \cdots + C_{n}^{2}\) in terms of \(n\).

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