There are N players in a tennis tournament. Assuming the initial pairings are done randomly, what are the odds that a certain pair will play each other?

Since there are N players, and each match eliminates one player, there are N-1 matches, as in a more familiar, simpler puzzle.

As there are C(N,2) possible pairings, the probability that a particular pairing will be included is (N-1)/C(N,2).  Since C(N,2)  = N*(N-1)/2, the desired probability reduces to 2/N.

This assumes that all competitors are equally skilled so that the outcome of each match is a 50-50 proposition.  Otherwise the most skilled are likely to participate in more rounds and therefore more matches (assuming no seeding, or byes, takes place), and the skill level of the particular pair would have to be taken into consideration.

Posted by Charlie on 2005-08-02 19:05:57