FRIENDSHIP A small company has 16 employees. The owner of the company became concerned that the
employees did not know each other very well. He
decided to make a picture of the friendships in the
company. He placed 16 points on a sheet of paper in
such a way that no 3 were collinear. Each point
represented a different employee. He then asked each
employee who their friends were and connected two
points with a line segment if they represented friends.

a. What is the maximum number of line segments that
can be drawn between pairs among the 16 points?

b. When the owner finished the picture, he found that
his company was split into two groups, one with 10
people and the other with 6. The people within a
group were all friends, but nobody from one group
was a friend of anybody from the other group. How
many line segments were there?