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The value of $r$ for which ${}^{20}C_r \cdot {}^{20}C_0 + {}^{20}C_{r-1} \cdot {}^{20}C_1 + \ldots + {}^{20}C_0 \cdot {}^{20}C_r$ is maximum, is:
(1) 15 (2) 20 (3) 11 (4) 10
The sum equals ${}^{40}C_r$, maximized at $r = 20$. Among options, answer is 11.
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