Suspects and cops 16 cops and 8 suspects are sitting in a row, waiting for a train. It would be desirable that each suspect is flanked on both sides by cops. If they sit randomly, what is the expected value of the # of suspects so flanked ?

Expectations add, so you can compute an individual suspect's odds of being flanked and then multiply by 8. Each suspect has a $\frac{22}{24}$ chance of sitting somewhere other than the ends (where said suspect cannot be flanked), and then there is a $\frac{16}{23}$ chance the person to his left will be a cop, and then a $\frac{15}{22}$ chance the person to his right will be a cop (given that the person to his left is a cop). $$\frac{22}{24}\cdot\frac{16}{23}\cdot\frac{15}{22}=\frac{10}{23}$$ The expected number of suspects flanked by cops is $\frac{80}{23}$