The number of triangles in a complete graph with 10 non-collinear vertices is

Step-by-step solution

Consider that there are m collinear points out of total n points in a plane. To construct a triangle we require 3 non-collinear points. Hence, the number of triangles will be n 3 - m 3 . Since, all the point in the above question are non-collinear, hence n=10 and m=0 Therefore, the total number of triangles are = 10 3 = 10 9 8 3 ! = 90 8 6 =15 8=120