If the sides AB , BC and CA of a triangle ABC have 3,5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

Question

If the sides AB , BC and CA of a triangle ABC have 3,5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to : (A) 364 (B) 240 (C) 333 (D) 360

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/0fcc735eced0031c8751060b972c0949-.png" /> Total Number of triangles formed = 14 C 3- 3 C 3- 5 C 3- 6 C 3 =333

Q. If the sides $A B, BC$ and $C A$ of a triangle $A BC$ have 3,5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

364

240

333

360

Total Number of triangles formed
$=^{14} C_{3} -^{3} C_{3} -^{5} C_{3} -^{6} C_{3}$
$= 333$

Q. If the sides AB,BC and CA of a triangle ABC have 3,5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

364

240

333

360

Total Number of triangles formed =14C3​−3C3​−5C3​−6C3​ =333

Q. If the sides $A B, BC$ and $C A$ of a triangle $A BC$ have 3,5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

Total Number of triangles formed
$=^{14} C_{3} -^{3} C_{3} -^{5} C_{3} -^{6} C_{3}$
$= 333$