A triangle PQR is such that 3 points lie on the side PQ , 4 points on QR and 5 points on R P respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?

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Correct answer: A. 205

Total no. of triangles formed aligned & = ¹² C ₃- ( ^3 C ₃+ ^4 C ₃+ ^5 C ₃ ) & = 12 11 10 9! 9! 3! -(1+4+10) & = 12 11 10 3 2 -15 & =2 110-15 & =220-15=205 aligned

A triangle PQR is such that 3 points lie on the side PQ , 4 points on QR and 5 points on R P respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?

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