Pascal's Triangle: A number of long, thin sticks are lying

A number of long, thin 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?

thanks for the help

b)
1.place one stick on xy plane in a on y axis
2. place second stick on plane so it differs by 1 degree. It crosses at one point
3. Place third stick at two degree angle relative to first, thus it crosses both sticks
4. place 4th stick at 3 degrees so that it crosses three sticks
5. place 5th stick at 4 degrees so it crosses the other 4 sticks
6. place 6th stick at 5 degrees so it crosses othe 5 sticks

number of intersections= 1*2*3*4*5
no.=5!

a)
number of intersections of n sticks is [n-1]!
Coefficients of Pascals triangle are kCn=n!/[k![n-k]!]
for k=1 and n=[n-1]
[n-1]!/[n-2]!

or the number of intersections =[n-2]! times the Pascal term for [n-1] things taken 1 at a time

I hope this is right
Arthur