Pesachim 79 - How many pure and how many not pure?

We often mentioned a situation where the community is not pure and is therefore allowed to bring the Passover sacrifice even in ritual impurity. But what do we mean by "community?" The whole world, Israel, Jerusalem? For this purpose, we only count those who have assembled for Passover to bring the offerings. Even here, we only need the majority. So, if more than half of those assembled to bring the offering are not ritually pure, everyone now brings it in impurity.

Also, if the Kohanim priests were impure, even though the community is pure, they all join and celebrate in impurity.

However, if only a minority of the community are impure, then the majority still celebrates, but the remaining minority gets a second chance thirty days later, on the so-called "Second Passover" or Pesach Sheni. 

Art: Jerusalem seen from Mount Josaphat by Auguste de Forbin