If ${ }^m{C}_r=0$ for $r>m$, then the sum $\sum _{r=0}^m{ }^{18}{C_r}^{20}{C}_{m-r}$ is maximum when m =

We have

$\sum _{r=0}^m{ }^{18}{C}_r{\times }^{20}{C}_{m-r}$

= Number of ways of choosing m persons out of 18 men and 20 women

${=}^{38}{C}_m$

Clearly, it is maximum when m = 19.