All possible orderings of ABC.

• To: mathgroup at smc.vnet.net
• Subject: [mg15689] All possible orderings of ABC.
• From: "Alan W.Hopper" <awhopper at hermes.net.au>
• Date: Mon, 1 Feb 1999 14:54:10 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Concerning Carlos Carreto's original message ;

>I am trying to construct all possible orderings  of  for example 3
>elements, where each element can be A, B or C.
>
>The result will be something like this: AAA
>AAB
>AAC
>ABA
>. . .
>CCC

Stephen Luttrell states ;

>I suspect that there might be a clever routine in
>DiscreteMath`Combinatorica` that does this directly, but I can't find
>it.

In[3]:= <<DiscreteMath`Combinatorica`

In[4]:=
Strings[{A,B,C},3]

Out[4]=
{{A,A,A},{A,A,B},{A,A,C},{A,B,A},{A,B,B},{A,B,C},{A,C,A},{A,C,B},{A,C,C},{B
,A,

A},{B,A,B},{B,A,C},{B,B,A},{B,B,B},{B,B,C},{B,C,A},{B,C,B},{B,C,C},{C,A,
A},{C,A,B},{C,A,C},{C,B,A},{C,B,B},{C,B,C},{C,C,A},{C,C,B},{C,C,C}}

In[5]:=
Length[%]

Out[5]=
27

But don't try to use the built-in String or StringForm, etc, for this
result.

--------------------

Alan Hopper

Katoomba, Australia.

```

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