Rabbi Yitzcḥok said: The Korban Pesach is slaughtered only in three groups of at least thirty people each.
We are uncertain if we need three groups of ten people at the same time or one after another.
Therefore, in order to satisfy both possible interpretations, we require three groups of thirty people each. This way we have both 3 groups of ten at one time and three groups of ten one after the next.
However using the correct procedure, fifty people are enough.
The procedure is: Thirty enter and slaughter, ten enter and ten of the original group leave, and then ten others enter and ten more leave. This way the Korban Pesach is considered to have been slaughtered in three groups of thirty people each, although the total number of people involved is only fifty.
My question is: What about after all three groups are done. May one then Shecht the Korban Pesach in solitude?
Let’s answer that question with another question. Why did the 2nd and third group need to be comprised of 30 people?
Since if the three groups need to be at once, this has already been accomplished, why can’t the 2nd and 3rd group consist of just ten each?
It is clear that even after the Korban was Shechted in 3 groups at one time, it must once again be slaughtered in 3 groups. Therefore the 2nd and 3rd group also needed to have thirty, so that they too can fulfil the Mitzva in 3 groups, even if those groups must be at once. We can therefore conclude that even after the three groups have already Shechted the Korban Pesach, it may not be Shechted in solitude, rather another three groups must be gathered.