1. There is a dispute about what preparations for the Korban Pesach may be done on Erev Pesach that falls on Shabbos.
2. The sons of Beseira forgot whether the Korban Pesach may be offered when Erev Pesach falls on Shabbos.
3. Hillel's correct answer to this question (#2) led him to be appointed the Nasi.
4. Hillel forgot the law in the case of a person who did not bring his slaughtering knife to the Beis ha'Mikdash before Shabbos.
5. The Gemara explains why the people were allowed to have an animal (see #4) carry a knife for them.
A BIT MORE
1. Rebbi Eliezer: Even preparations that could have been done before Shabbos override Shabbos. Rebbi Akiva: Only preparations that may not be done before Shabbos override Shabbos.
2. They asked Hillel, who replied that just as the Korban Tamid is offered on Shabbos, the Korban Pesach also overrides Shabbos. This is derived from the fact that in both cases the verse says, "in its time."
3. Besides his knowledge, he had also learned under the tutelage of the two great Rabbis of that generation, Shemayah and Avtalyon.
4. On Pesach of that year, the people stuck the knife in the wool of the animal or between its horns in order to avoid carrying it.
5. Since one is not allowed to do work with an animal dedicated to be a Korban, the people would withhold from dedicating the animal as a Korban until they actually arrived at the Beis ha'Mikdash. While one is generally not allowed to dedicate a Korban on Shabbos, one is allowed to do so with the Korban Pesach.