Eight points are selected at random from the interior of a unit circle.
What is the probability that these eight points constitute the eight vertices of a convex octagon?
Who am I kidding? A much simpler version of this extremely difficult problem popped up a few years ago in perplexus, entitled "Four Pins and a rubber band
". It was beyond our ability to do when n = 4. and it is exponentially more difficult now that n = 8.
Here is the link
to the solution at Wolfram for n = 4. The n = 8 situation is not covered.