Six odd parts summing to 96

Count the solutions of $x_1+x_2+\dots+x_6=96$ in which every $x_i$ is an odd non-negative integer. The count equals $\binom{n}{k}$ with $k<n/2$; report $nk$.

$250$. Writing $x_i=2y_i+1$ turns the equation into $y_1+\dots+y_6=45$ with $y_i\ge0$. Stars and bars gives $\binom{50}{5}$, so $nk=50\cdot5=250$.