80% chance of having same birthday...
Yesterday at dinner my friends told me that if there is a room with 40 people in it, that there is an 80% chance that two of them have the same birthday. I was initially skeptical as most would be, so I did the math...
Now those that of you that haven't seen counting theory in a while may find this hard to swallow but...
a = 365^40 is the total number of combinations of birthdays that 40 people can have.
b = permutation(365,40) are the total number of combinations of birthdays where no two people share a birthday.
the mathematical formula for that permutation is 365!/(365-40)!.
so our final formula for the percent chance that two people share a birthday is expressed as follows:
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