Question

On a triangle ABC, on the side AB, 5 points are marked, 6 points are marked on the side BC and 3 points are marked on the side AC (none of the points being the vertex of the triangle). How many triangles can be made by using these points?

• A. 90
• B. 333
• C. 328
• D. None of these

Answer 1

The correct option is B 333

There will be two types of triangles
The first type will have its vertices on the three sides of the $\Delta ABC$.
The second type will have two of its vertices on the same side and the third vertex on any of the other two sides.
Hence, the required number of triangles
$=6\times 5\times 3{+}^6{C}_2\times 8{+}^5{C}_2\times 9{+}^3{C}_2\times 11$
= 90 + 120 + 90 + 33
= 333