Birthday Paradox

Whats the birthday paradox?
How many people should be there in a room so that there is 50% chance that two people share the same birthday?

Solution:
Lets assume its not a leap year.
Let P be the probability where none of them share a birthday. Then (1 – P) is the probability where atleast 2 of them share a birthday.

For n people, if they do not share a birthday, the first one can have 365 options, the second one 364..etc etc
hence, P = ( 365 * 364 * 363 * ….. * (365 – n) ) / 365^n.

Here, I need some kind of a program to figure out the n. The answer came out to be 23. P came to be 0.49. 1-P = 0.50. Thats 50% chance.