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MathGroup Archive 2004

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Re: Creating combinations from a group of sets

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48715] Re: Creating combinations from a group of sets
  • From: koopman at sfu.ca (Ray Koopman)
  • Date: Fri, 11 Jun 2004 03:52:44 -0400 (EDT)
  • References: <ca91bp$t8h$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Jeanette L Domber <Jeanette.L.Domber at aero.org> wrote in message 
news:<ca91bp$t8h$1 at smc.vnet.net>...
> I have a group of sets:
> 
> {1,2,3}
> {4,5}
> {6}
> {7,8}
> 
> I wish to create all unique combinations of the sets that contain exactly one element from each set:
> 
> {1,4,6,7}
> {1,5,6,7}
> {1,4,6,8}
> {1,5,6,8}
> {2,4,6,7}
> {2,5,6,7}
> etc.
> 
> In all, there should be 12 combinations.

In[1]:= a = {{1,2,3},
             {4,5},
             {6},
             {7,8}};

In[2]:= Distribute[a,List]
Out[2]= {{1,4,6,7},
         {1,4,6,8},
         {1,5,6,7},
         {1,5,6,8},
         {2,4,6,7},
         {2,4,6,8},
         {2,5,6,7},
         {2,5,6,8},
         {3,4,6,7},
         {3,4,6,8},
         {3,5,6,7},
         {3,5,6,8}}


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