There are 5 points P_1, P_2, P_3, P_4, P_5 on the side A B, excluding A and B, of a triangle A B C. Similarly there are 6 points P_6, P_7, …, P_11 on…

There are $\displaystyle 5$ points $\displaystyle P_1, P_2, P_3, P_4, P_5$ on the side $\displaystyle A B$, excluding $\displaystyle A$ and $\displaystyle B$, of a triangle $\displaystyle A B C$. Similarly there are $\displaystyle 6$ points $\displaystyle \mathrm{P}_6, \mathrm{P}_7, \ldots, \mathrm{P}_{11}$ on the side BC and $\displaystyle 7$ points $\displaystyle \mathrm{P}_{12}, \mathrm{P}_{13}, \ldots, \mathrm{P}_{18}$ on the side CA of the triangle. The number of triangles, that can be formed using the points $\displaystyle \mathrm{P}_1, \mathrm{P}_2, \ldots, \mathrm{P}_{18}$ as vertices, is: