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Re: Arrangements

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108910] Re: Arrangements
  • From: dh <dh at metrohm.com>
  • Date: Tue, 6 Apr 2010 08:21:35 -0400 (EDT)
  • References: <hpf5iu$orh$1@smc.vnet.net>

On 06.04.2010 13:23, John wrote:
> Google 6, Windows-Xp
>
> The number of different arrangements of sixteen symbols -- eight
> letters A and eight letters B -- is Binomial[16,8]=12870. Is there a
> command that will generate all 12870 arrangements one at a time
> without duplication? Any order is acceptable.
>
> I used RandomSample[Range[16]] to select a random permutation of
> sixteen different symbols. Assigning the letter A to the first eight
> numbers in the random permutation and the letter B to the last eight
> letters in the permutation created a randomly selected arrangement.
> Awkward, but it works because Binomial[2n,n](n!)(n!)=(2n)!).
>
> John
>
Hi John,
you may create all arrangements in one go by:
Needs ["Combinatorica`"];
t = DistinctPermutations[Join[Table["a", {8}], Table["b", {8}]]];
cheers, Daniel

-- 

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>



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