(Q). Consider a polygon of n sides. what is the number of triangles that can be drawn taking vertices of these polygons as vertices of triangles and no side of triangles is common with any side of the polygon?
Solution:-
Without any restriction number of tiangle formed is ⁿC₃
Now from ths value reduce the number of triangles which are being counted in this value but actually they are not desired, now consider the following cases:
case(i): Number of triangles having three sides common with the sides of polygon is 0.
case(ii): Number of triangles having two sides common with the sides of polygon is n.
case(iii): Number of triangles having one side common with the sides of polygon
