Pesachim 70B

במרובה. מנא ידעי?

with few people registered for it, so that each person receives a large portion of the offering. Therefore, there is no need for a Festival peace-offering or for a cleaver. The Talmud questions this answer: How do the owners know already on the 13th that only a small number of people will be registered for the Paschal lamb? Perhaps more people will register for the offering before it is slaughtered, in which case we should assume that the cleaver was immersed, as it might be necessary to bring a Festival peace-offering together with the Paschal lamb.

ואלא שבא בטומאה. סוף סוף, מנא ידעי?

Rather, we must say that we are talking about a Paschal lamb that came in a state of ritual impurity, in which case a Festival peace-offering is not brought, and consequently there is no need for a cleaver. The Talmud asks: Ultimately, how do the owners know already on the 13th when they are immersing their knives that the Paschal lamb will be brought in ritual impurity, so that they need not immerse their chopping knives? Perhaps it will turn out that most of the community is ritually pure.

דמית נשיא. דמית נשיא אימת? אילימא דמית בשלשה עשר ⁠— סכין למה לי דמטבליה? ואלא דמית בארבעה עשר. מאי שנא סכין דמטביל, ומאי שנא קופיץ דלא מטביל לה?

The Talmud answers that we are talking about a situation where the Nasi died, in which case all of Israel must defile themselves in order to participate in his burial. The Talmud asks: When did the Nasi die? If you say that he died on the 13th and everyone became ritually impure as a result, why do I need to immerse the slaughtering knife to begin with? It will become ritually impure again in any event. Rather, he died on the 14th and they did not know in advance that the Paschal lamb would be brought in a state of impurity. But if so, what is different about the slaughtering knife that he immerses it and what is different about the cleaver that he does not immerse it?