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Counting & ProbabilityHardIdentities and Techniques, Proved

Identities and Techniques, Proved · Hard problem

A 5-element subset of {1,2,…,20}\{1,2,\ldots,20\} is chosen at random. An element xx of the subset is isolated if neither x−1x-1 nor x+1x+1 is in the subset. What is the expected number of isolated elements? Express your answer as a common fraction.