birthday problem (factorial limit)

On 28-Sep-08 17:51:55, Uwe Ligges wrote:

J?rg Gro? wrote:

Hi,
I tried to calculate the formula for the birthday problem
(the probability that at least two people out of a group of
n people share the same birthday)

But the factorial-function allows me only to calculate
factorials up to 170.

So is there a way to push that limit?

to solve this formula:

(factorial(365) / factorial((365-23))) / (365^23)

Obviously you can easily rewrite this formula to:

prod(343:365) / (365^23)

or

factorial(23) * choose(365, 23) / (365^23)

Uwe Ligges

(n=23)

I would put it in an even "safer" form:

n <- 23
prod( ((365-(n-1)):365)/rep(365,n) )

In other word: It evaluates

 (343/365)*(344/365)* ... *(365/365)

365^N --> "Inf" if N > 120, whereas

  n<-150
  prod( ((365-(n-1)):365)/rep(365,n) )
# [1] 2.451222e-16

Best wishes,
Ted.