Twenty five of King Arthur's knights are seated at their customary round table. Three of them are chosen - all choices being equally likely - and are sent off to slay a troublesome dragon. Let be the probability that at least two of the three had been sitting next to each other. If is written as a fraction in lowest terms, what is the sum of the numerator and the denominator?
This problem is copyrighted by the American Mathematics Competitions.
Instructions for entering answers:
For questions or comments, please email email@example.com.