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There are 5 points $P_{1}, P_{2}, P_{3}, P_{4}, P_{5}$ on the side AB excluding A and B of a triangle ABC ,similarly there are 6 points $P_{6}, P_{7}, . . ., P_{11}$ on side BC and 7 points $P_{12}, P_{13}, . . ., P_{18}$ on the side CA of the triangle .The number of triangles that can be formed using the point to $P_{1}, P_{2}, . . ., P_{18}$ as vertices

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796

771

776

751

answer is B.

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Detailed Solution

$\begin{array}{l} 18_{C_{3}} - 5_{C_{3}} - 6_{C_{3}} - 7_{C_{3}} \\ = 751 \end{array}$

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