Question

How many distinct rays can be formed from 50 collinear points?

Answer 1

If the rays must lie in the line containing the 50 points, then since a ray is defined by its starting point and its direction, I'd go with
50+50 = 100
Many of the rays will overlap, but since they have distinct starting points, I'd count them as different.

But if the rays can go in any direction, there are infinitely many rays starting at each of the 50 points.

Now, if you mean line segments, then we have a counting problem, basically a variation on how many diagonals in an n-sided polygon (which problem can be found online)

Answer 2

Thank you oobleck.

I think they have to go through though. I'm assuming that could be a 100 but I have a formula in mind. Do you think it's applicable "2+(n−2)×2"