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MathGroup Archive 2010

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Arrangements

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108886] Arrangements
  • From: John <jwa0 at lehigh.edu>
  • Date: Tue, 6 Apr 2010 07:23:15 -0400 (EDT)

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


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