What are the chances?

SM provides the idea for this post. Pardon us for the math...

In a group of people of size r, what is the probability that two people share the same birthday? (Discounting leap days...)

TC = Total potential combinations of unique birthdays = 365 * 364 * 363 * ... * 365-r+1.

Probability of all unique birthdays = TC / (365^^r).

Probability of not all unique birthdays = 1 - (TC/(365^^r)).

Some examples:

# people	Prob (all unique)	Prob (not all unique)
----------	-----------------	---------------------
1	1.000	0
10	0.883	0.117
20	0.5885	0.4115
30	0.293	0.707
40	0.1087	0.8913