Question

The sides \( AB \), \( BC \), and \( CA \) of a triangle \( \triangle ABC \) have respectively 3, 4, and 5 points lying on them. The number of triangles that can be constructed using these points as vertices is

• A. 205
• B. 220
• C. 210
• D. None of these

Hint:

To find the number of triangles from given points, use combinations to select points from each side.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
The number of triangles that can be formed is given by selecting 3 points from the 3 sides. The calculation uses combinatorics and the number of ways to select points on each side.

Step 2: Conclusion.
The total number of triangles that can be formed is 205, corresponding to option (1).