(Q). Consider a set of 8 non-overlapping triangle in a plane such that no three points in the plane is collinear then
(i). if all the possible triangle are drawn taking vertices of these triangles such that not more than 1 point is selected from a triangle then find the total number triangle hence drawn?
(ii). Find the total number of new triangles that can be drawn from this system of triangles?
Solution:-
(i).
3 trignle out of 8 triangle can be selected in ⁸C₃ ways
& now one vertices from each of these 3 selected triangle can be selected in ³C₁ ways
Hence required number of triangle
= ⁸C₃׳C₁׳C₁׳C₁ Answer
(ii).
total points in plain = 8×3 = 24
total nubmer of triangle drawn is ²⁴C₃ but out of these 8 are original triangles. Hence number of new triangle is
= ²⁴C₃ – 8 Answer