Permutations And Combinations

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 \(\mathrm{P}_6, \mathrm{P}_7, \ldots, \mathrm{P}_{11}\) on the side \(\mathrm{BC}\) and 7 points \(\mathrm{P}_{12}, \mathrm{P}_{13}, \ldots, \mathrm{P}_{18}\) on the side \(\mathrm{CA}\) of the triangle. The number of triangles, that can be formed using the points \(\mathrm{P}_1, \mathrm{P}_2, \ldots, \mathrm{P}_{18}\) as vertices, is: