Question

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

• A. $210$
• B. $205$
• C. $215$
• D. $220$

Answer 1

Answer: (B)

$205$

Answer 2

Required number of triangles $= ^{12}C_{3} - \left( ^{3}C_{3}+ ^{4}C_{3}+ ^{5}C_{3}\right) = 205$