Mathematics - Permutation & Combination Question with Solution | TestHub

Line $L_1$ of slope 2 and line $L_2$ of slope $\frac{1}{2}$ intersect at the origin O . In the first quadrant, ${\mathrm{P}}_1,{\mathrm{P}}_2,\dots .{\mathrm{P}}_{12}$ are 12 points on line $L_1$ and $Q_1,Q_2,\dots ..Q_9$ are 9 points on line $L_2$. Then the total number of triangles, that can be formed having vertices at three of the 22 points $\mathrm{O},{\mathrm{P}}_1,{\mathrm{P}}_2,\dots {\mathrm{P}}_{12}$, ${\mathrm{Q}}_1,{\mathrm{Q}}_2,\dots .{\mathrm{Q}}_9$, is: