John Calvin Commentary Numbers 3:15

"Number the children of Levi by their fathers` houses, by their families: every male from a month old and upward shalt thou number them." — Numbers 3:15 (ASV)

Number the children of Levi after the house of their fathers. The enumeration of the tribe now follows, beginning with the three sons of Levi—Kohath, Gershon, and Merari—from whom many families afterwards descended.

It must be observed, however, that all Levites were numbered down to the youngest infants, whereas for the rest of the people, only those who had passed their twentieth year were included in the count. This method of counting initially made the tribe of Levi appear to be the smallest.

However, by having the infants counted, God intended to maintain a just proportion, as we shall see. For if He had only counted the Levites who were above their twentieth year, the total number of firstborn Israelites would not have been known, and thus the compensation to be made for them would have been uncertain.

This gracious provision should have encouraged the people to pay the tribute for the surplus more readily. For since, after the calculation was made, it was clear how much the number of Levites fell short of the total number of Israelite firstborn, God justly willed that those firstborn who exceeded the Levites in number should be redeemed for money, who would otherwise have been transferred to the tribe that represented the firstborn. It would have been a perverse act to refuse God what He demanded, especially when He had so graciously agreed to such a just arrangement.

There was also another reason why the Levites were included in the census from their earliest childhood, unlike the others: namely, because it was not necessary for them to be fit for war, since God enrolled soldiers for Himself from the rest of the people, who would later bear arms.