Question

If PQRS is a convex quadrilateral with 3, 4, 5 and 6 points marked on sides PQ, QR, RS and PS respectively, then the number of triangles with vertices on different sides is

• A. 220
• B. 270
• C. 342
• D. 282

Answer 1

Answer: (C)

Total number of triangles = Number of triangles with vertices on sides PQ, OR and RS+ Number of triangles with vertices on sides OR, RS and PS + Number of triangles with vertices on sides RS, PS and PQ + Number of triangles with vertices on sides PS. PQ and QR ${=}^3{C}_1{\times }^4{C}_1{\times }^5{C}_1{\times }^4{C}_1{\times }^5{C}_1{\times }^6{C}_1$ $+{}^5{C}_1{\times }^6{C}_1{\times }^3{C}_1{+}^6{C}_1{\times }^3{C}_1{\times }^4{C}_1$ $=60+120+90+72=342$