Re: Creating combinations from a group of sets

• To: mathgroup at smc.vnet.net
• Subject: [mg48712] Re: Creating combinations from a group of sets
• From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
• Date: Fri, 11 Jun 2004 03:52:39 -0400 (EDT)
• References: <ca91bp\$t8h\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```This does what you want:

sets = {{1, 2, 3}, {4, 5}, {6}, {7, 8}};
Flatten[Outer[List, Apply[Sequence, sets]], 3]
Steve Luttrell

"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.
>
> If I use KSubsets giving it a list {1,2,3,4,5,6,7,8} to create
combinations containing 4 elements, I get a list of 70 combinations, 58 of
which are extraneous to my application.
>
> Does anyone know how to manipulate the functions in
DiscreteMath`Combinatorica` to accomplish this efficiently?
>
> Thanks,
>     Jeanette
>

```

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