Probabilitical Players

Discrete Mathematics Level 4

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.

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