To make a triangle 3 non-collinear points are required Non-collinear points are = 7 - 3 = 4 Triangle can be formed from the points = (3 from non-collinear points), or (2 from non-collinear and 1 from collinear), or (1 from non-collinear and 2 from colinear) Ways of selecting of 3 points out of 4 non-collinear points =‌4C3=4 Ways of selecting of 2 points out of 4 non-collinear points =‌4C2=6 Ways of selecting of 1 point out of 4 non-collinear points =‌4C1=4 Ways of selecting of 1 point out of 3 collinear points =‌3C1=3 Ways of selecting of 2 points out of 3 collinear points =‌3C2=3 Hence the number of triangles formed N=4+(6×3)+(4×3) N = 4 + 18 + 12 = 34