1) "EIN KORBAN TZIBUR CHALUK"
QUESTION: The Gemara cites several Beraisos that teach that if most of the people are Tamei, then the entire Tzibur may offer the Korban Pesach in a state of Tum'ah. The reason for this is the principle, "Ein Korban Tzibur Chaluk" -- a Korban Tzibur, which may be brought in a state of Tum'ah, is not "divided" and brought by different groups in different states of Tum'ah or Taharah.
These Beraisos seem to contradict the concept of "Tum'ah Dechuyah b'Tzibur." As RASHI earlier (77a, DH Dechuyah) explains, "Tum'ah Dechuyah b'Tzibur" means that there is no absolute allowance to freely offer the Korban in a state of Tum'ah, but rather the prohibitions against Tum'ah are merely pushed aside in the event of great necessity. This is in contrast to the opinion that maintains "Tum'ah Hutrah b'Tzibur," which means that the Torah's prohibitions of Tum'ah do not apply at all when the Tzibur is Tamei (and not that they do apply but they are merely pushed aside).
The Gemara in Yoma (7b) explains that when some of the Kohanim of the Beis Av (the group of Kohanim designated to perform the Avodah on that day) are Tamei and others are Tahor, the ones who are Tahor must offer the Korban whether Tum'ah is Hutrah or Dechuyah. However, when all of the Kohanim of the Beis Av are Tamei, the opinion that "Tum'ah Dechuyah b'Tzibur" maintains that Kohanim from other Batei Avos who are Tahor should be sought to perform the Avodah, while the opinion that "Tum'ah Hutrah b'Tzibur" maintains that the Kohanim of this Beis Av may bring the Korban despite the fact that they are Tamei.
According to this, why may the people who are Tahor offer the Korban in a state of Tum'ah when the majority of the people are Tamei? Since they are Tahor, they should be required to offer it in a state of Taharah. Why does the Gemara here say that those who are Tahor may offer it in a state of Tum'ah because the minority follows the majority? The Tana here presumably maintains that "Tum'ah Dechuyah b'Tzibur," as the Gemara implies earlier (77a).
ANSWER: The Gemara explains that the reason why the entire Tzibur is permitted to offer the Korban Tzibur in a state of Tum'ah when a minority of members of the Tzibur are Tahor is because "Ein Korban Tzibur Chaluk," a public offering is not divided. This reasoning applies only once it has been determined that the Korban must be offered b'Tum'ah. Until that point, however, every attempt must be made to avoid bringing the Korban b'Tum'ah, such as by finding Kohanim who are Tahor to perform the Avodah with knives and other instruments that are Tahor. Only once it has been determined that the Korban will be offered in a state of Tum'ah (since the Kohanim are Tamei, or since a majority of the people will have to eat the Korban b'Tum'ah) does the rule of "Ein Korban Tzibur Chaluk" permit the rest of the Tzibur, who are Tahor, to offer it b'Tum'ah as well.
For this reason, there is a difference between a case in which the Kohanim and Klei Shares become Tamei, and a case in which the people who are eating the Korban Pesach become Tamei, as a number of Acharonim point out (see GEVUROS ARI to Yoma 6b, RASHASH to Temurah 14a, DEVAR SHMUEL here in Mahadura Basra). When the Kohanim or Klei Shares become Tamei, the normal laws of "Tum'ah Dechuyah b'Tzibur" apply, because it is possible to avoid bringing the Korban b'Tum'ah in the first place (as the Gemara here makes clear). However, when the people become Tamei, it is inevitable that the Korban will be eaten in a state of Tum'ah. Therefore, a new rule applies: a Korban Tzibur may not be divided. This is implicit in the Mishnah that says that the Korban Pesach is brought b'Tum'ah when "Rov" (a majority) of the people are Tamei, or when "the Kohanim" are Tamei. The Mishnah does not mention "Rov," a majority, with regard to the Kohanim, because when a majority of the Kohanim are Tamei it is still prohibited to offer the Korban b'Tum'ah, since a Kohen who is Tahor is available to offer it.
However, the RAMBAM (Hilchos Bi'as ha'Mikdash 4:14) rules that the principle of "Tum'ah Hutrah b'Tzibur" also applies when most, but not all, of the Kohanim are Tamei: "If most of the Kohanim in Yerushalayim are Tamei at the time of the offering of the Korban, then it may be brought b'Tum'ah." (The RAMBAM reiterates this in Hilchos Kidush ha'Chodesh 4:6, and in Perush ha'Mishnayos to Temurah 2:1 and Pesachim 7:4.)
The Rambam's words are difficult to understand. Why should it be permitted to offer a Korban b'Tum'ah because most of the Kohanim are Tamei? It is possible to avoid offering the Korban b'Tum'ah in the first place by having the Kohanim who are Tahor perform the Avodah! In addition, the Rambam himself (Hilchos Bi'as ha'Mikdash 4:12 and Perush ha'Mishnayos to Pesachim 7:4) allows any Korban Tzibur to be offered b'Tum'ah when most of the people are Tamei. Why should the state of Tum'ah of the people affect a Korban Tzibur other than the Korban Pesach (which much be eaten by every member of the nation)? Why should the Kohanim be allowed to offer the Korban Tamid (which is not eaten at all) b'Tum'ah, just because most of the people are Tamei? As long as there are Kohanim who are Tahor, they should bring the Korban in a state of Taharah!
These questions are raised by the GEVUROS ARI (ibid.) and the RASHASH (ibid.), who leave them unanswered. (See, among others, the OR SAME'ACH in Hilchos Bi'as ha'Mikdash 4:12 and in Hashmatos at the end of Sefer Avodah, who addresses these questions.)
2) WHEN HALF THE PEOPLE ARE "TAMEI" AND HALF ARE "TAHOR"
QUESTION: The Korban Pesach must be brought on the fourteenth of Nisan. However, the Torah provides a dispensation for those who were too far away and were not able to reach Yerushalayim on time, or who were Tamei when the fourteenth of Nisan arrived. They may bring the Korban Pesach on the fourteenth of Iyar. This dispensation, though, applies only to individuals. If the entire Tzibur was Tamei, the Korban Pesach is brought on the fourteenth of Nisan, even though the people are in a state of Tum'ah and will offer the Korban b'Tum'ah.
The Gemara discusses the Halachah in a case in which half of the Tzibur is Tamei and half is Tahor. Everyone agrees that the people who are Tahor bring the Korban on Pesach Rishon, the fourteenth of Nisan. When, though, do the people who are Tamei bring the Korban? The Gemara here records three opinions.
Rav says that the people who are Tamei also bring the Korban on Pesach Rishon. Rav Kahana, in the Gemara's first version of his statement, says that they bring the Korban on Pesach Sheni, the fourteenth of Iyar. In the Gemara's second version of his statement, Rav Kahana says that those who are Tamei do not bring the Korban Pesach at all.
A fourth opinion is cited by the Gemara later. Rebbi Yehudah in the Beraisa (80a) says that the entire Tzibur may bring their Korban b'Tum'ah (this differs from Rav's opinion, who says that those who are Tahor must bring the Korban b'Taharah). (See Chart.)
The Gemara here (79b) cites a Beraisa which states explicitly that those who are Tamei bring the Korban on Pesach Sheni, like Rav Kahana (according to the Gemara's first version of his statement). How do the other opinions (Rav, and the second version of Rav Kahana) understand this Beraisa?
The Gemara answers that the Beraisa does not refer to a case in which exactly half of the people are Tahor and half are Tamei. Rather, it refers to a case in which a majority of the people are Tahor. Why, then, does it say that half are Tahor? The Gemara explains that in the case of the Beraisa, there are a number of women who are Tamei, who raise the total number of Tamei people to match the number of Tahor people. Thus, when the Beraisa says that "half of the people are Tahor and half are Tamei," it means that half are Tamei when the women who are Tamei are included. Since a woman's Mitzvah to bring the Korban Pesach is voluntary (both on Pesach Rishon and on Pesach Sheni if she was Tamei on Pesach Rishon), the number of women are not counted when we determine how many members of the Tzibur are Tahor and how many are Tamei. Consequently, the group that is Tamei is a minority, and the group that is Tahor is the majority. Since those who are Tamei are a minority, they bring the Korban Pesach on Pesach Sheni.
Why does the Gemara not suggest the opposite scenario in order to answer the Beraisa? There is an opinion that women are obligated to bring the Korban Pesach (on both Pesach Rishon and on Pesach Sheni if they were Tamei on Pesach Rishon), just like men. Accordingly, when the Beraisa says that half of the Tzibur are Tahor and half are Tamei, it is counting only the men. There are, however, some women who are Tahor, and because they are obligated to bring the Korban Pesach they are included in the count, and thus they make those who are Tahor the majority. (This is similar to the way the Gemara resolves another Beraisa.) (MAHARSHA)
ANSWER: The KARNEI RE'EM suggests that if women are obligated on both Pesach Rishon and Pesach Sheni, then they are absolutely equal to men with regard to the Korban Pesach and there is no reason for the Beraisa to count only the men and say that half are Tahor and half are Tamei. Only if women would be obligated to bring the Korban only on Pesach Rishon but not on Pesach Sheni, or they would have no obligation to bring the Korban on either day, would they not be considered to have an equal standing with men with regard to the Korban Pesach, and the Beraisa would be justified in counting only the men. If women are fully obligated just like men, then the words "half are Tahor and half are Tamei" must also include the women. Therefore, the Gemara does not suggest this answer to explain the Beraisa.