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

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 (A) 220 (B) 215 (C) 210 (D) 205

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a68573e1d0cfabb5c3797f6cc5e43edf-.png" /> Number of triangles = 12 C 3-(1+ 4 C 3+ 5 C 3) = 220 - 15 = 205

Q. On the sides $A B, BC, C A$ of a $△ A BC, 3, 4, 5$ 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

220

215

210

205

Number of triangles $=^{12} C_{3} - (1 +^{4} C_{3} +^{5} C_{3})$
$= 220 - 15 = 205$

Q. On the sides AB,BC,CA of a △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

220

215

210

205

Number of triangles =12C3​−(1+4C3​+5C3​) =220−15=205

Q. On the sides $A B, BC, C A$ of a $△ A BC, 3, 4, 5$ 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

Number of triangles $=^{12} C_{3} - (1 +^{4} C_{3} +^{5} C_{3})$
$= 220 - 15 = 205$