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From: nachum@uiucdcs.UUCP
Newsgroups: net.math
Subject: Re: permuting 0123456789
Message-ID: <28200053@uiucdcs.UUCP>
Date: Mon, 18-Feb-85 22:17:00 EST
Article-I.D.: uiucdcs.28200053
Posted: Mon Feb 18 22:17:00 1985
Date-Received: Thu, 21-Feb-85 07:23:12 EST
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Nf-ID: #R:ihnet:-20100:uiucdcs:28200053:000:263
Nf-From: uiucdcs!nachum    Feb 18 21:17:00 1985


Such permutations are called "derangements".
The number of derangements of n items is

                   k
            n  (-1)              -1
        n! sum ----- = round(n! e  )
           k=0  k!

The problem is solved, for example, in Knuth vol. 1 p. 177ff.