A) 215
B) 342
C) 225
D) 424
Correct Answer: B
Solution :
| the number of triangles with vertices on sides \[AB,BC,CD={}^{3}{{C}_{1}}\times {}^{4}{{C}_{1}}\times {}^{5}{{C}_{1}}\]Similarly for other cases |
| \[\therefore \]The total number of triangles |
| \[={}^{3}{{C}_{1}}\times {}^{4}{{C}_{1}}\times {}^{5}{{C}_{1}}\times {}^{3}{{C}_{1}}\times {}^{4}{{C}_{1}}\times {}^{6}{{C}_{1}}\]\[+{}^{3}{{C}_{1}}\times {}^{5}{{C}_{1}}\times {}^{6}{{C}_{1}}+{}^{4}{{C}_{1}}\times {}^{5}{{C}_{1}}\times {}^{6}{{C}_{1}}=342\] |
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