Question

PQRS is a quadrilateral having $3,4,5,6$ points in PQ, QR, RS and SP respectively. The number of triangles with vertices on different sides is?

• A. $220$
• B. $270$
• C. $282$
• D. $342$

Answer 1

Answer: (D)

$342$

The number of triangles with vertices on side, $AB,BC,CD=3C_1\times 4C_1\times 5C_1$

$\therefore$ Total no. of triangles $=3C_1\times 4C_1\times 5C_1+3C_1\times 4C_1\times 6C_1+3C_1\times 5C_1\times 6C_1+4C_1\times 5C_1\times 6C_1=3\times 4\times 5+3\times 4\times 6+3\times 5\times 6+4\times 5\times 6=342$