Re: 3 Birthday problem (again)!

In article
<3ec1bd5d-144f-4280-9a5e-d52fcf84c1e9@[EMAIL PROTECTED]
>,
Phoe6 <orsenthil@[EMAIL PROTECTED]
> wrote:

> Question: There are 27 students on the debate team. What is the
> probability that at least 3 of them have their birthday in the same
> month.
> 
> From inspection, we can understand that as there are more than 24
> students ( 2 x 12 for months), there will be 3 students extra who will
> have to share their birthday with the any of the others, so the chance
> is 1.
> 
> I am looking for the mathematical equations for this.
> How does 'at least three' of them share the birthday translate to in
> this?
> 

It's the pigeonhole principle : If 27 pigeons are in 12 pigeonholes
then some pigeonhole must contain at least ciel(27/2) = 3 pigeons [
ciel(x) is the the smallest integer larger than x].

See
<http://mathworld.wolfram.com/DirichletsBoxPrinciple.html>

-- 
Paul Sperry
Columbia, SC (USA)