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Probability of 3 people in a room of 30 having the same birthday

The birthday paradox is a common problem about the probability that any 2 people from a random set of $N$ people share any common birthday. My question is a generalisation: What is the probability that $M$ people from a random set of $N$ people share any common birthday. The only difference is generalising 2 to $M$.

I'm particularly interested in the case where $M=5$ if that makes it significantly easier to solve for.

Henry
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moinudin
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    http://math.stackexchange.com/questions/25876/probability-of-3-people-in-a-room-of-30-having-the-same-birthday/25878#25878 –  Aug 17 '11 at 14:51
  • See also Section 1.2 on page 2 here: http://www.math.ucsd.edu/~tkemp/180A/180A.LectureNotes.pdf – Shai Covo Aug 17 '11 at 15:08

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