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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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