MathDB

In a skiing jump competition

65

contestants take part. They jump with the previously established order. Each of them jumps once. We assume that the obtained results are different and the orders of the contestants after the competition are equally likely. In each moment of the competition by a leader we call a person who is scored the best at this moment. Denote by

p

the probability that during the whole competition there was exactly one change of the leader. Prove that

p > 1/16

Problem Statement