If you hold K-K at a 10 person table, the probability that one of your opponents has A-A is 9 * 6/C(50,2) - C(9,2)/C(50,4) or about 4.39%. Not exactly complex.
Inclusion/Exclusion Principle
That question, along with the 3 doors problem, was asked basically every other day for a year. It has been analyzed to death, brought back from death, and analyzed to death again, more times than you can imagine. Any other question is met with open arms. The only ones that are problematic are the questions that have 100 threads pertaining to them, and are easily found with the search function.