Jamieson, Fausset and Brown on 1 Chronicles 24:6

6. one principal household--The marginal reading is preferable, "one house of the father." The lot was cast in a deliberate and solemn manner in presence of the king, the princes, the two high priests, and the chiefs of the priestly and Levitical families. The heads of families belonging to Eleazar and Ithamar were alternately brought forward to draw, and the name of each individual, as called, registered by an attendant secretary. To accommodate the casting of the lots to the inequality of the number, there being sixteen fathers' houses of Eleazar, and only eight of Ithamar, it was arranged that every house of Ithamar should be followed by two of Eleazar, or, what is the same thing, that every two houses of Eleazar should be followed by one of Ithamar. If, then, we suppose a commencement to have been made by Eleazar, the order would be as follows: one and two, Eleazar; three, Ithamar; four and five, Eleazar; six, Ithamar; seven and eight, Eleazar; nine, Ithamar; and so forth [Bertheau]. The lot determined also the order of the priests' service. That of the Levites was afterwards distributed by the same arrangement (1Ch 24:31).