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## Re: lynx-dev Options, V.Links, random

 From: Doug Kaufman Subject: Re: lynx-dev Options, V.Links, random Date: Tue, 21 Dec 1999 07:16:00 -0800 (PST)

```On Tue, 21 Dec 1999, Doug Kaufman wrote:

> Correct formula for chance of duplicate values (20 from pool of 10000)
>
> 1 - ( 9999! / (9980! * 10E76 * 20!))
>
> It certainly is humbling to be so wrong in public. Thanks for not

I guess that I should also learn not to reply after midnight when I
haven't had much sleep the night before. Now that I have had some
sleep, I believe that the first equation I posted was correct. Look
at a reductionist case, 3 draws out of a pool of 5. After one draw
the result is always unique. After a second draw, there is 4/5 chance
that it is still unique, regardless of order. After a third draw, the
chance that it is still unique is (4/5)*(3/5).

The number of possible combinations, drawing 20 out of 10000 is
(10E80 /20!). The number of unique combinations, drawing 20 out of
10000 is (10000! / (9980! * 20!)). Hence the chance of a unique
combination is:

((10000! / (9980! * 20!)) / (10E80 / 20!))

which reduces to:

(10000! / (9980! * 10E80))
or
(9999! / (9980! * 10E76))

So I still think that the chance of a duplicate filename would be:
1 - (9999! / 9980! * 10E76)

It looks like the chance of a unique permutation is the same as the
chance of a unique combination. Any corrections to this would be
appreciated.
Doug

__
Doug Kaufman