1. Tardigrade
  2. Question
  3. Mathematics
  4. On the sides AB , BC , CA of a triangle ABC , 3,4,5 distinct points (excluding vertices A , B , C ) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. On the sides $AB , BC , CA$ of a $\triangle ABC , 3,4,5$ distinct points (excluding vertices $A , B , C$ ) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are

Permutations and Combinations

Solution:

image
Number of triangles $={ }^{12} C _3-\left(1+{ }^4 C _3+{ }^5 C _3\right)$
$= 220 - 15 = 205$