A) 220
B) 270
C) 342
D) 282
Correct Answer: C
Solution :
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 \[{{=}^{3}}{{C}_{1}}{{\times }^{4}}{{C}_{1}}{{\times }^{5}}{{C}_{1}}{{\times }^{4}}{{C}_{1}}{{\times }^{5}}{{C}_{1}}{{\times }^{6}}{{C}_{1}}\] \[+{{\,}^{5}}{{C}_{1}}{{\times }^{6}}\,{{C}_{1}}{{\times }^{3}}\,{{C}_{1}}{{+}^{6}}{{C}_{1}}{{\times }^{3}}\,{{C}_{1}}{{\times }^{4}}{{C}_{1}}\] \[=60+120+90+72=342\]
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