<pre>
Assume people are selected at random, and that their birthdays are
uniformly and independently distributed over the 365 days of the year
excluding Feb. 29.

Think instead about the probability, among n people, that none of them
share a birthday. For a set of one person, the odds that he/she shares
a birthday with no one else in the set is 1. Adding a 2nd person, the
person can have 364 of 365 possible birthdays. Adding the 3rd, he/she
can have any of 363 b'days, etc. So the desired expression for the odds
that no one shares a b'day is:

  365 ''' 364 ''' ... * 365 - n + 1 / 365 ^ n

and subtract that from 1 to get the odds that two people share a birthday.

For n <code> 22, this gives a probability of .476, and n </code> 23 gives .507.

references

M. Klamkin and D. Newman, Extensions of the birthday surprise, J. Comb. Th. 3 (1967), 279-282.

see [[Coupon]]

see [[Line]]
</pre>
