# Probabilitical Players

Sixteen players $$S_{1}, S_{2}, ..., S_{16}$$ play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assume that all the players are of equal strength.

Find the probability that exactly one of the two players $$S_{1}$$ and $$S_{2}$$ is among the eight winners.

The probability is in the form $$\frac{a}{b}$$. Find a + b.