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The sum $\sum_{i = 0}^{m} (\begin{matrix} 10 \\ i \end{matrix}) (\begin{matrix} 20 \\ m - i \end{matrix}) (where (\begin{array}{l} p \\ q \end{array}) = 0$ if $p < q)$ is maximum where $m$ is

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Correct option is C

We have ∑i=0m 10i20m−i = the number of ways of choosing m persons out of 10 men and 20 women = the number of ways of choosing m persons out of 30 persons =30CmBut 30Cm is maximum for m = 15.

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The sum ∑i=0m 10i20m−i (where pq=0 if p < q) is maximum where m is

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The sum $\sum_{i = 0}^{m} (\begin{matrix} 10 \\ i \end{matrix}) (\begin{matrix} 20 \\ m - i \end{matrix}) (where (\begin{array}{l} p \\ q \end{array}) = 0$ if $p < q)$ is maximum where $m$ is