--- On Thu, 5/2/09, Inna Becher wrote:
> the formula I need is actually:
>
> probability=1- [comb(n-m,k)/comb(n, k)]
> so I have useful numbers after the computation. (n=180000,
> m=2, k=2000)
(n-m)!
comb(n-m,k) = -----------
k! (n-m-k)!
n!
com(n,k) = ---------
k! (n-k)!
so:
(n-m)!
-----------
k! (n-m-k)!
comb(n-m,k)/comb(n,k) = ---------------
n!
---------
k! (n-k)!
(n-m)! k! (n-k)!
= ----------------
k! (n-m-k)! n!
(n-m)! (n-k)!
= -------------
(n-m-k)! n!
ln(comb(n-m,k)/comb(n,k)) =
ln((n-m)!) + ln((n-k)!) - ln((n-m-k)!) - ln(n!)
As comb(n-m,k)/comb(n,k) = exp(ln(comb(n-m,k)/comb(n,k))) you can compute your probability by typing:
scalar n = 180000
scalar m = 2
scalar k = 2000
di 1- exp(lnfactorial(n-m) + lnfactorial(n-k) - lnfactorial(n-m-k) - lnfactorial(n))
-- Maarten
-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting address:
Buitenveldertselaan 3 (Metropolitan), room N515
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
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