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The value of $\sum_{r=0}^{6} \binom{6}{r} \cdot {}^{6}C_{6-r}$ is equal to:
(1) 1124 (2) 1324 (3) 1024 (4) 924
This is the coefficient of $x^6$ in $(1+x)^{12}$, which is ${}^{12}C_6 = 924$.
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