Birthday probability solution

Solution to the problem of finding the probability of at least two people having the same birthday

Solution to birthday probability problem: If there are n people in a classroom, what is the probability that at least two of them have the same birthday?
General solution:
P = 1-365!/(365-n)!/365^n
If you try to solve this with large n (e.g. 30, for which the solution is 29%) with the factorial function like so:
P = 1-factorial(365)/factorial(365-30)/365^30
Matlab will output NaN because Matlab tries to compute very large values here.
The approach in this script is to start from n=1 and at each step use the previous step's result to avoid dealing with large numbers.