(Q). Consider vertices of an octagon & mid point of its sides (total 16 points). How many triangles can be drawn taking these 16 points as vertices of the triangle?
Solution:-
Without any restriction we can get maximum ¹⁶C₃ triangles.
From this we have to reduce the number of triangles that we can not get if three points are collinear this can happen in ⁸C₁׳C₃ = 8 ways.
So total number of such triangles = ¹⁶C₃ – 8 Answer
