Each telephone call passes through a number of switching offices before reaching its destination. The number and types of switching offices in the United States in 1971 were estimated to be as follows:

Note that the type of switching office in the local exchange of the originating call is fixed. Let n be the number of switching offices encountered (other than the local exchange) by a telephone call. Assuming that each switching office is randomly and independently chosen from the population, determine the probability that the call passes through exactly ni (i = 1, 2, 3, 4) switching offices of type i, where n1 + n2 + n3 + n4 = n. Determine the marginal pmf for each type of office.