An arriving plane carries r families. A total of nj of these families have checked in a to...

An arriving plane carries r families. A total of nj of these families have checked in a total of j pieces of luggage, . Suppose that when the plane lands, the  pieces of luggage come out of the plane in a random order. As soon as a family collects all of its luggage, it immediately departs the airport. If the Sanchez family checked in j pieces of luggage, find the expected number of families that depart after they do.