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The sum $\sum_{i = 0}^{m} (\begin{array}{l} 10 \\ i \end{array}) (\begin{array}{l} 20 \\ m - i \end{array})$ is maximum when m is

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answer is C.

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Detailed Solution

$\begin{array}{rcl} \sum_{1 = 0}^{M} 10 C_{i} 20_{C_{m - 1}} \\ = & 10_{C_{0}} 20_{C_{m}} + 10_{C_{1}} 20_{C_{m - 1}} + . . . . + 10_{C_{m}} 20_{C_{m}} \\ = & 30_{C_{m}} \\ 30_{C_{m}} is maximum if m = 15 \end{array}$

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