Binomial Coefficient of Binomial Coefficients

\[\displaystyle \Large\binom{\binom{a}{b}}{\binom{c}{d}} = 0 \]

How many ordered 4-tuples of integers \( (a,b,c,d) \) between 0 and 10 inclusive are there such that they satisfy the equation above?

Notation: Binomial Coefficient.

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