Offering the Korban Pesach with intent for those who are not registered to eat it, or who are not eligible to eat it would disqualify the sacrifice. Unless some of the people who are part of that intent can eat, at least or the mishnah. The question of a mixed crowd – valid and not valid to eat the Korban Pesach – complicates matters, but salvages the karbanot. Also: The Gemara cites a passage from the Tosefta of a parallel case to the mishnah, wherein the kohen’s intent was for the wrong group. As well as bringing the biblical verses that recognize the expanding groups that are possible for the Korban Pesach. What if those who are not eligible to eat from the Korban Pesach were included by intending them to do “zerikat ha-dam” – the sprinkling of the blood on the altar? Well, that’s a fine machloket between Rabbah and R. Hisda. Perhaps it is not resolved (at least thus far) because it remains theoretical.
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