8. N people arrive separately to a professional dinner. Upon arrival, each person looks to see if he or she has any friends among those present. That person then either sits at the table of a friend or at an unoccupied table if none of those present is a friend. Assuming that each of the $$(\frac{N}{2})$$ pairs of people are, independently, friends with probability p, find the expected number of occu-

pied tables.

HINT: Let X_i equal 1 or 0 depending on whether the i^th arrival sits at a previously unoccupied table.