A total of N peeple arrive separately to a professional dinner. Upon arrival, each of the N persons 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 pair of people are, independently, friends with probability 3), nd a simple expression for the expected number of occupied tables as a function of p. Find the limit of this expression as p > 0 (all persons are surely strangers) and p > 1 (all persons are surely friends). Hint: Let Xi equal 1 or 0 dependent on whether the ith arrival sits at a previously unoccupied table, for i=1,2,...,N