Project Euler Problem 906
Three friends attempt to collectively choose one of n options, labeled 1,dots,n, based upon their individual preferences
Solution
Answer: 0.0195868911
Using a combinatorial analysis of the Condorcet-winner condition for three random preference permutations, one can derive an exact summation formula for $P(n)$ and evaluate it numerically for $n=20,000$.
The resulting value is:
Answer: 0.0195868911