MathDB
Only one local maximum

Source:

August 29, 2010
probabilitycombinatorics proposedcombinatorics

Problem Statement

In an urn there are n balls numbered 1,2,,n1, 2, \cdots, n. They are drawn at random one by one without replacement and the numbers are recorded. What is the probability that the resulting random permutation has only one local maximum? A term in a sequence is a local maximum if it is greater than all its neighbors.