SOLUTION: How many distinct line segments are formed by connecting 20 collinear points?

Each segment is uniquely defined by a pair of its ending points;

and inversely, each pair of ending points uniquely determines the segment.


Here the pairs of ending points are considered as unordered pairs.


So, the number of segments is equal to the number of unordered pairs of 20 points, which is


     = 10*19 = 190.     ANSWER