Question 104
At lunch, Abby, Bart, Carl, Dana, and Evan share a pizza divided radially into $16$ slices. Each one takes one slice of pizza uniformly at random, leaving $11$ slices. The remaining slices of pizza form "sectors" broken up by the taken slices, e.g. if they take five consecutive slices then there is one sector, but if none of them take adjacent slices then there will be five sectors. What is the expected number of sectors formed?