Message-ID: <XFMail.080928190942.Ted.Harding@manchester.ac.uk>
Date: 2008-09-28T18:09:42Z
From: (Ted Harding)
Subject: birthday problem (factorial limit)
In-Reply-To: <48DFC43B.3060604@statistik.tu-dortmund.de>
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.
--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 28-Sep-08 Time: 19:09:40
------------------------------ XFMail ------------------------------