birthday paradox

I was going throught the question that what is the minimum batch size required in a system to ensure that two people at least have the same birthdays and did a simulation of that in excel.
However, I thought that if we can have a maxima or minima funda in P(n)=1-365!/(365-n)!*365^n we can find the value of n.
The answer is 50 approx.
Let us see.