(i). If no three points out of 15 points lie on a line, then the number of lines is 15C2 as exactly one line is drawn through two points. Since 6 out of 15 points are collinear, they from only one line instead of 6C2 lines. Hence the number of lines gets decreased by 6C2 -1. Hence the required number of lines
= 15C2 -(6C2 -1) = 105 -15+1 = 91
(ii). A triangle is formed by joining 3 non-collinear points. So if the 15 points are all non-collinear, 15C3 triangles can be formed. But here 4 points lie on a line and form no triangle instead of 6C3. Thus the required number of triangles
= 15C3 -6C3 = 455 -20 = 435