It seems that Elizabeth was a descendant from the house of Aaron, of the tribe of Levi (since her husband was a priest). Her cousin was Mary, who was from the house of David or at least we assume that when we compare the genealogies in Matthew 1:1-16 and Luke 3:23-28.
So we know that Mary and Elizabeth were related, but we don’t know how. They were cousins, yes, but the Greek word used for cousin (syngenis) can be used for “first cousins,” “second cousins,” “third cousins” or any other numbered cousins.
Also, the mothers of Mary and Elizabeth could have been sisters but not from the same tribe. The only requirement for Levitical priesthood was for the male, not the female.
Thus, theu could have been related as cousins and from different tribes themselves.
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