A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
1 Chronicles 24:1
ch1 24:1DIVISION OF THE SONS OF AARON INTO FOUR AND TWENTY ORDERS. (1Ch. 24:1-19)
Now these are the divisions of the sons of Aaron--(See on Ch1 23:6).
1 Chronicles 24:2
ch1 24:2Nadab and Abihu died before their father--that is, not in his presence, but during his lifetime (see Num 3:4; Num 26:61).
therefore Eleazar and Ithamar executed the priest's office--In consequence of the death of his two oldest sons without issue, the descendants of Aaron were comprised in the families of Eleazar and Ithamar. Both of these sons discharged the priestly functions as assistants to their father. Eleazar succeeded him, and in his line the high priesthood continued until it was transferred to the family of Ithamar, in the person of Eli.
1 Chronicles 24:3
ch1 24:3Zadok . . . and Ahimelech of the sons of Ithamar--This statement, taken in connection with Ch1 24:6, is not a little perplexing, since (Sa2 15:24, Sa2 15:35; Sa2 20:25) Abiathar is mentioned as the person conjoined in David's time with Zadok, in the collegiate exercise of the high priesthood. Some think that the words have been transposed, reading Abiathar, the son of Ahimelech. But there is no ground for regarding the text as faulty. The high priests of the line of Ithamar were the following: Ahiah or Ahimelech, his son Abiathar, his son Ahimelech. We frequently find the grandfather and grandson called by the same name (see list of high priests of the line of Eleazar, Ch1 6:30-41). Hence the author of the Chronicles was acquainted with Ahimelech, son of Abiathar, who, for some reason, discharged the duties of high priest in David's reign, and during the lifetime of his father (for Abiathar was living in the time of Solomon, Kg1 2:27) [KEIL].
1 Chronicles 24:4
ch1 24:4there were more chief men found--The Hebrew may be translated, "There were more men as to heads of the sons of Eleazar." It is true, in point of fact, that by the census the number of individuals belonging to the family of Eleazar was found greater than in that of Ithamar. And this, of necessity, led to there being more fathers' houses, and consequently more chiefs or presidents in the former.
1 Chronicles 24:5
ch1 24:5Thus were they divided by lot--This method of allocation was adopted manifestly to remove all cause of jealousy as to precedence and the right of performing particular duties.
1 Chronicles 24:6
ch1 24:6one 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 (Ch1 24:31).