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If $\sum_{r=0}^{25} \left{{}^{50}C_r \cdot {}^{50-r}C_{25-r}\right} = K\binom{50}{25}$, then $K$ is equal to:
(1) $(25)^2$ (2) $2^{25} - 1$ (3) $2^{24}$ (4) $2^{25}$
$K = 2^{25}$.
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