One principal household being taken for Eleazar— That is, one of the principal families of Eleazar was first taken, and then one of Ithamar's, and thus alternately till the whole was finished. See Houbigant's note.
Related Commentaries of 1 Chronicles 24:6
1 Chronicles 24:6
6 And Shemaiah the son of Nethaneel the scribe, one of the Levites, wrote them before the king, and the princes, and Zadok the priest, and Ahimelech the son of Abiathar, and before the chief of the fathers of the priests and Levites: one principala household being taken for Eleazar, and one taken for Ithamar.