A Zimun is recited before Birkat Hamazon when three people ate a meal together. According to the Shulhan Aruch, even a minor – who has not yet reached the age of Bar Misva – can count as the third person for a Zimun, provided that he is capable of reciting Birkat Hamazon and understands to whom he recites the Beracha. Children who have reached the age of nine years are generally assumed to have reached this point.
Ashkenazim have the custom not to count boys to a Zimun before they reach the age of Bar Misva. The Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909), however, writes that the practice in Baghdad followed the Shulhan Aruch’s view, allowing minors to count toward a Zimun, and this is indeed the Halacha for Sepharadim. Thus, once a child reaches this point in his educational development, he may join two adults in forming a Zimun. Likewise, if nine men are present, he may count as the tenth person to allow the group to recite Hashem’s Name ("Elokenu") in the Zimun.
A woman cannot join with two men to form a Zimun, as this would violate proper standards of modesty. However, if three or more women eat by themselves, then, according to some opinions, they are required to recite a Zimun, while others maintain that this is optional. The Ben Ish Hai concludes that it is proper for women in such a case to recite a Zimun (listen to audio recording for precise citation). Women do not, however, recite a Zimun with Hashem’s Name ("Elokenu"), even if ten or even one hundred women eat together.
If women eat a meal where three or more men are present, the women should not recite Birkat Hamazon before the men. They must instead wait until the men recite Birkat Hamazon so that they can participate in the Zimun. Even though they do not count toward the Zimun, they nevertheless bear the obligation to recite the Zimun together with the men.
It is proper for a host to ask his guest to lead the Zimun. If one of his guests is a Kohen, then that guest take precedence over others in leading the Zimun. A Torah scholar takes precedence over a Kohen, and, of course, a Torah scholar who is a Kohen takes precedence over other Torah scholars. If a Torah scholar who is not a Kohen leads the Zimun in the presence of Kohanim, he should say, "Bireshut Ha’kohanim," asking permission from the Kohanim to lead the Zimun.
Some people offer a Levi precedence over others when no Kohanim are present. This is not, however, the prevalent practice, and one is not required to grant a Levi precedence over a Yisrael in leading the Zimun.
Summary: The custom of the Sepharadim is to allow a boy to join with two adults to form a Zimun, provided that the boy is old enough to recite Birkat Hamazon and to understand the concept of Birkat Hamazon. (This is generally assumed to be the case once a child reaches the age of nine.) Women do not join with two men to form a Zimun, but three women who eat a meal together should make a Zimun. If women eat together with three or more men, they should not recite Birkat Hamazon until they recite the Zimun together with the men. A guest should recite a Zimun, and a Kohen takes precedence over others, with the exception of Torah scholars, who take precedence over Kohanim.
