Charles Ellicott Commentary 1 Chronicles 24:6

"And Shemaiah the son of Nethanel the scribe, who was of the Levites, wrote them in the presence of the king, and the princes, and Zadok the priest, and Ahimelech the son of Abiathar, and the heads of the fathers` [houses] of the priests and of the Levites; one fathers` house being taken for Eleazar, and one taken for Ithamar." — 1 Chronicles 24:6 (ASV)

And Shemaiah ... wrote them. —Made a list of the names in the order determined by lot, as given below (1 Chronicles 24:7–18).

The chief of the fathers. —Better, the heads of the houses or clans.

One principal household being taken ... —The Hebrew text is corrupt. However, we may, with great probability, restore the original reading by changing a single letter and translating it as: one clan was drawn for Eleazar, and one drawn for Ithamar: that is, alternately.

One Hebrew manuscript supports this reading. The Septuagint has, “one by one for Eleazar, and one by one for Ithamar.” (Some Hebrew manuscripts concur. The Syriac and Vulgate read, “one house for Eleazar, and another house for Ithamar.”)

The chances would be that the Ithamarites would all be drawn before the Eleazarites. (Compare to 1 Chronicles 25:22–31, where ten “sons of the Hemanite” are left over and drawn last.)