Here's what I recall of the question from CNML Grade 11, 2010/2011 Contest #3, Question 7:
There are 2010 points on a circle, evenly spaced. Ford Prefect will* randomly choose three points on the circle. He will* connect these points to form a shape. What is the probability that the resulting shape will* form a right angled triangle?
I answered $\frac{1}{4} = 25\%$, but that's probably incorrect. (Right?)
When I got home, I thought it out in my head, and I got this:
$\frac{2010 * (2010/1005)}{2010 \choose 3}$
$\frac{2020050}{1351414120} = \frac{3015}{2017036} = 0.149476756984010201\%$
I'm probably wrong ...again. Can anyone tell how to get the right answer (if I'm not wrong :) )?
*in the past of the future of the perfect present present time double into ripple fluctuater byer doininger of the past future continuum...
EDIT: Realized my mistake in copying the question.