Question

There are three parallel straight lines. Two points, 'A' and 'B', are marked on the first line, points, 'C' and 'D' are marked on the second line; and points, 'E' and 'F', are marked on the third line. Each of these 6 points can move to any position on its respective straight line. 

Consider the following statements: 

1. The maximum number of triangles that can be drawn by joining these points is 18. 

2. The minimum number of triangles that can be drawn by joining these points is zero.

Which of the statement(s) given above is/are correct? 

(a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2

Answer 1

(b) Maximum number of triangles can be formed by selecting 3, 4 or 5 points out of 6 at a time. 

So, maximum no. of triangles = ⁶C₃ + ⁶C₄ + ⁶C₅ which is clearly more than 18. Now, triangles formed will be minimum i.e., zero, when the points will overlap on the same line and all the points are along the same vertical line.