Question: (When a Pasul was mixed with Kosher Korbanos, why can't we offer them?) We should force them to go away (so animals will separate from the mixture elsewhere, not in front of us), and each that separates is (presumably) from the majority!

Answer (Rava): Chachamim decreed not to do so, lest someone take in a way (i.e. from the mixture) that is considered Kavu'a.

Pesachim 88b Version #1 (Mishnah): If Reuven forgot which Korban Pesach was for him, he is exempt from Pesach Sheni.

(Abaye): This is only if he forgot after Zerikah, for at the time of Zerikah there was potential for him to eat from it, but not if he forgot before Zerikah, for at the time of Zerikah he could not eat from it.

Version #2 (Beraisa): If the skins of the Pesachim of five groups became mixed, and a wart was found on one of them, all of the Pesachim are burned, and the groups are exempt from Pesach Sheni.

(Abaye): This is only if the skins became mixed after Zerikah, for at the time of Zerikah there was potential (to identify the Pasul Korban, and for the other groups) to eat from it. If they became mixed before Zerikah, they bring Pesach Sheni (for at the time of Zerikah no group could eat from it).

In version #1, (even though both Korbanos are Kesherim,) Abaye requires that he remembered at the time of Zerikah. All the more so, he requires that the skins were not mixed before Zerikah;

In Version #2, he is stringent if the skins were mixed before Zerikah, but lenient if Reuven forgot before Zerikah. Since both Korbanos are Kesherim, and if he will remember later they may be eaten, and it is clear to Hash-m (i.e. there is no intrinsic Pesul), they are Yotzei.

Menachos 42b (Rav Shmuel bar Rav Yehudah): When making Techeiles dye, to see if it finished cooking, we put some in an eggshell, and dye a tuft of wool in it. We spill out the dye in the eggshell and burn the tuft.

Inference: A dyed sample is Pasul (for Techeiles) because the dying must be Lishmah. If the sample dye would be returned to the pot, it would disqualify all the dye inside.

Sanhedrin 79b (Mishnah - R. Shimon): If people sentenced to be stoned became mixed with people sentenced to be burned, we stone them, for this is more lenient;

Chachamim say, we burn them, for this is more lenient.

Bava Metzia 6b (Mishnah): If an animal already counted (during tithing) jumped back into the pen and was mixed with the uncounted animals, they are all exempt.

This shows that a Safek is not tithed.

Tosfos (71a Sof DH Afilu): When people sentenced to be stoned were mixed with people sentenced to be burned, we give the more lenient death. Rabbeinu Yitzchak questioned this, for even in capital cases we follow the majority! We do not exempt a murderer due to the possibility that there already was a hole where he stabbed the victim! R. Tam answered since in any case we kill him, we do not follow the majority to be stringent. Alternatively, we do not follow the majority to Vadai obligate stoning him. If one murderer who was not sentenced to death were mixed with murderers who were sentenced, all are exempt. We do not follow the majority to do something that is Vadai Sheker, i.e. to kill all of them. This is unlike one who Vadai killed, but we are unsure if he killed a healthy person or a Tereifah. Also, we can say that it (the case of a murderer not sentenced who got mixed with sentenced murderers) is a Safek Kavu'a, so it is considered an even Safek (without a majority). He is exempt, for we are lenient about Safek Nefashos. We do not make them go away so that one will separate from the mixture (in our absence, not in the place of Kevi'us) and say that he came from the majority, for we may not do so to be stringent on him. Also, we decree not to do so, lest one take directly from the mixture. Rashi (Menachos 42b DH u'Te'imah) says that if test dye was poured back into the pot, it disqualifies the entire pot. This is because Bitul cannot make it considered Lishmah.

Or Some'ach: Even though the Isur (the murderer not sentenced) is not recognizable, Bitul does not apply to people, therefore it is like an Isur Kavu'a.

Ha'aros on Shirei Berachah (YD 279:3): Bitul makes Isur as if it is not, but we have no source that Bitul b'Rov helps for Mitzvos to make something considered Lishmah. The Rashba says that when dry things mix, Bitul b'Rov teaches that what is in front of us is Heter. Therefore, one person may eat all three pieces one after the other. If Sifrei Torah became mixed, Bitul b'Rov can teach that any one is Kosher, but not that all are Kosher.

Rashi (73b DH Nichbeshinhu): The Gemara suggested that we force them to wander, so they will not be in the place of Kevi'us.

Tosfos (73b DH v'Nichbeshinhu): If one separates in our absence, not in the place of Kevi'us, we do not consider it like a Safek Kavu'a, i.e. an even Safek. Rather, we follow the majority.

Shitah Mekubetzes (73b:1): The Gemara suggested that we turn away, so we will not see when one of them separates, and then it is not considered Kavu'a. The Sar mi'Kutzi says that Isur Kavu'a is only when it is known in its place. Here it is not; because living animals are important, we consider it like a known Isur. Therefore, even if one separates in front of us, since they left their Kevi'us, we can say that it came from the majority.

Question (Tosfos 6b DH Kafatz): When one of the animals already counted jumped back into the pen, it should be Batel in the majority (of animals that were not yet counted), and all should be liable to be tithed! It is only mid'Rabanan that something that is counted is not Batel. Kavu'a applies only when the Isur and Heter are known, but one does not know from which he took, e.g. nine stores (sell Kosher meat, and one sells Neveilah). I explained in Chulin that it is not considered a Briyah (which is never Batel). Do not say that only one animal remained in the pen (so there is no majority), for 'amidst them' connotes unlike this.

Oneg Yom Tov (4): I am unsure whether Bitul helps for something Pasul because an action was not done. E.g. if Matzah was not baked Lishmah, Bitul in a majority of Matzos Lishmah will not give it the attribute of Lishmah. Therefore, all the mixed Matzos are Pasul for the Mitzvah. Chavas Da'as (101) asked from five Korbanos Pesach that were mixed, and a wart was found on one. None may be eaten. Why don't we follow the majority, and permit all to be eaten? Bitul removes an Isur, but it does not make something considered a Kosher Korban. Since the wart disqualifies, the Shechitah and Zerikah needed to make a Kosher Korban were not done.

Achiezer (YD 15): Kehilas Yakov, Chavas Da'as (101) and Beis Efrayim (YD 33) asked why the Pasul Korban Pesach is not Batel in the Kosher ones. Why must they bring Pesach Sheni if they became mixed before Zerikah? Also, what is the Kal va'Chomer from the Mishnah to the Beraisa? In the Mishnah, only two Korbanos were mixed, so one may not eat them. In the Beraisa, five were mixed, so the majority permits eating it! Some answer that since only the owners of a Pesach may eat it, each Korban is forbidden to most of them. Even according to the opinion that Isurim are Mevatel each other, this is only to exempt from lashes, but surely one may not eat it! I say that we are stringent even if one recognizes his Korban Pesach, but the skins are mixed, and we do not know which had the wart. Each should be able to say that his came from the majority. Even though it is Kavu'a, R. Shimshon holds that a Kavu'a Isur that is not Nikar is forbidden only mid'Rabanan even when Bitul does not apply. (Eglah Arufah, i.e. a calf to atone for a found murdered corpse, forbids farming the Nachal (valley or river) where it is beheaded.) This explains why we may farm a Nachal without concern lest an Eglah Arufah was beheaded there, even though Bitul does not apply to land. (The Torah permits, and Chachamim did not forbid.) The Oneg Yom Tov's answer explains why it is not considered a Kosher Korban, but not why they may not eat it. I explain that the question was because it is Kavu'a that is not Nikar. Bitul does not give attributes of the Mevatel only when we seek to permit due to Bitul. When we say 'what separates comes from the majority', it attains the attributes of the Mevatel. A case occurred in which one of the people arranging the dough was a Nochri, who does not work l'Shem Matzas Mitzvah. I said that regarding the buyer, we assume that the Matzah came from the majority, which were made Lishmah. Tosfos (Bava Metzia 6b) proves this. He asked that when one of the animals already counted returned to the pen, it should be Batel among the animals that were not yet counted. How can Bitul b'Rov give it the attribute of being liable to be tithed?! I say that Tosfos asked that we should make them go away so that animals will separate from the mixture, and say that what separates comes from the majority. Then, it attains the attributes of the Mevatel. This is like Tosfos and the Shitah Mekubetzes in Zevachim. Therefore, even if the Pesachim became mixed before Zerikah, and they were Kevu'im at the time, we can say that each came from the majority, and we can offer it. Even if we will say that this is like one who asks about himself and his friend (we know that one of them became Tamei in Reshus ha'Rabim; normally we are lenient about such a Safek, but we cannot be Metaher both of them), this is a stringency mid'Rabanan. The Torah permits such a case. Further, it seems that this stringency does not apply when there is a majority. We permit a majority even if later he will eat the minority (in spite of the contradiction). Perhaps Isurim are not Mevatel each other only regarding Isurim like Pigul, Nosar and Tamei, which are forbidden to everyone. Here, a Pesach forbidden to one (who has no share in it) is permitted to others (its owners). If one vowed from a food and it became mixed with Chelev and blood, surely the food helps to be Mevatel them, for the food is permitted to others. Automatically, it is Batel also for the one who vowed. If he ate the food, he is exempt for Chelev and blood. Therefore, it is as if the blemished Pesach is mixed with Heter. There is no source to say that it should not be Batel. Isurim are not Mevatel each other to permit eating because each bit has some Isur on it. This does not apply here.