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May 10th, 2007, 08:38 AM  #1 
Newbie Joined: May 2007 Posts: 2 Thanks: 0  Possible exhaustive groupings of N objects?
I have a question: If you have N objects, what is the possible number of ways that you can exhaustively group them (i.e. group them without having any objects left over?) For example: for N = 2; there are 2 possible groupings: [AB] [A] + [B] for N = 3; there are 5 possible groupings: [ABC] [AB] + [C] [AC] + [B] [BC] + [A] [A] + [B] + [C] for N=4, there are (I think) 15: [ABCD] [ABC]+[D] [ABD]+[C] [ACD]+[B] [BCD]+[A] [AB]+[CD] [AB]+[C]+[D] [A]+[B]+[CD] [BC]+[AD] [BC]+[A]+[D] [B]+[C]+[AD] [AC]+[BD] [A]+[C]+[BD] [AC]+[B]+[D] [A]+[B]+[C]+[D] Any help would be greatly appreciated. Thanks, Ed 
May 10th, 2007, 11:38 AM  #3  
Newbie Joined: May 2007 Posts: 2 Thanks: 0 
I think you're right. I saw this before, but was thrown by the main title. Looking lower, it does say: Quote:
[ABC] + [] + [] [AB] + [C] + [] [AC] + [B] + [] [BC] + [A] + [] [A] + [B] + [C] is equivalent to [ABC] [AB] + [C] [AC] + [B] [BC] + [A] [A] + [B] + [C] ...at least for calculating the number of possible solutions. I found a nice description is on the WikiPedia: http://en.wikipedia.org/wiki/Partition_of_a_set Thanks a lot for your help! Ed  

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