A family has just moved to a new city and requires the services of both an obstetrician and a pediatrician. There are two easily accessible medical clinics, each having two obstetricians and four pediatricians. The family will obtain maximum health insurance benefits by joining a clinic and selecting both doctors from that clinic. In how many ways can this be done? Denote the obstetricians by 01, 02, 03, and 04 and the pediatricians by P,..,Pg. Then we wish the number of pairs (Oj, Pj) for which 0; and P; are associated with ---Select--- V clinic. Because there are four obstetricians, n = and for each there are four choices of pediatrician, so n2 . Applying the product rule gives N = n, n2 = X possible choices. =