ABCD is a convex quadrilateral.3,4,5&6 points are marked on the sides AB,BC, CD and DA respectively the no. of triangles formed with vertices on different sides is

The number of triangles with vertices on side AB, BC, CD = 3C1×4C1×5C1
Similarly for other cases
The total number of triangles = 3C1×4C1×5C1 + 3C1×4C1×6C1 + 3C1×5C1×6C1 + 4C1×5C1×6C1
3C1=3!1!2!3C1=3!1!2!=3=3
4C1=4!1!3!4C1=4!1!3!=4=4
5C1=5!1!4!5C1=5!1!4!=5=5
6C1=6!1!5!6C1=6!1!5!=6=6
⇒3×4×5+3×4×6+3×5×6+4×5×6⇒3×4×5+3×4×6+3×5×6+4×5×6
⇒342