A number of long, think sticks are lying in a pile at odd angles such that the sticks cross each other. a) relate the maximum number of intersection points of n sticks to entries in Pascal's triangle. b) What is the maximum number of intersection points with six overlapping sticks?

My work:

a) 2 sticks -- 1 Point of intersection
3 sticks -- 3 points of intersection
4 sticks-- 4
5 sticks-- 8