Question: A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is
Options:
(A) 7
(B) 8
(C) 9
(D) 24
(E) 23 Let's think first. Some random reasoning:
To construct 2 lines, three points can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third line goes from the third-point to the first point, a triangle is formed, and if it goes to the fourth point, a triangle is not formed. So, there are 24 ways to form a triangle and 24 ways of avoiding triangle. The final answer: (D).