In Happy Birthday, the question was if there are N people in a room, what is the probability that there are at least two people in the room who share a birthday?

What if instead exactly two was required? If there are N people in a room, what is the probability that there are exactly two people in the room who share a birthday?

(Note: Assume leap year doesn't exist, and the birthdays are randomly distributed throughout the year.)

(In reply to re(2): thoughts by Bob Smith)

Why is it that it is the nth person that shares a birthday with someone else?  Why not for example, the 10th person out of 30 matches the 15th out of the 30 people?

Posted by Charlie on 2006-06-09 14:57:45