How and when was the census done to determine how many of each category? Probably people were arriving all day long (from within 15 mil), so they probably could not do a census in the morning. I suspect Bais Din needed to determine prior to the first Korban in the afternoon. Further, they must have trusted every one's answer to the question if they are tamei or tahor, since they did not have time to investigate. I would like to have some where I could read about this subject (Hebrew or English) thanks
Benyomin Hoffman, Los Angeles, CA
You are correct that they determined this when everyone was already gathered to enter the Azarah for the first group of people who bring the Korban Pesach, as stated by the Rambam (Hilchos Korban Pesach 7:6). The Tzlach in Pesachim (94b) says that even if afterwards other people arrived for the later groups and the numbers changed, it would not matter. The status was only determined before the first group started to offer the Pesach. The main Gemara on this topic is on the bottom of 94b (see commentaries there).
Interestingly, the Rambam (ibid.) says that they counted based on people entering the Azarah, not based on people who would be eating the Korban Pesach.
They clearly trusted the answers of the people entering, as during the Regel the law is that "Kol Yisrael Chaveirim," meaning that everyone is considered to be a Chaver and is trusted regarding the laws of purity and impurity (see Chagigah 26a).
All the best,
Yaakov Montrose