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March 21st, 2010, 05:24 AM  #1 
Newbie Joined: Mar 2010 Posts: 10 Thanks: 0  Question on Combinations
I understand that if i were to choose 4 from S={1,2,3,4,5,6} then it'd be 6C4. But, I have a situation where I have to list up all 4 multiset combinations for S={1,1,2,2,3,4}. I'm confused and do not know what to do since the formulas do not work on this. Please help. Thanks~ 
March 21st, 2010, 05:04 PM  #2 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: Question on Combinations
What is a multiset combination?

March 21st, 2010, 06:10 PM  #3 
Newbie Joined: Mar 2010 Posts: 10 Thanks: 0  Re: Question on Combinations
Multiset is a set where you have repetition of an individual in that set. ie. S={1,1,2,2,3,4} is a multiset where there are repetition of 1s and 2s. 
March 22nd, 2010, 01:22 PM  #4 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: Question on Combinations
Oh, sure. Let's look at a simpler case. If we have {1, 2, 3, 4, 5, 5} and we choose 2, how many do we have? Well, if we only choose at most 5, we have 5 choose 2 ways. If we get both fives, we have exactly one choice. 
March 23rd, 2010, 06:39 AM  #5 
Newbie Joined: Mar 2010 Posts: 10 Thanks: 0  Re: Question on Combinations
I'm sorry but I do not understand what you are saying. I had a look at an example and the combination for S= {1,1,2,2,3,4} is 8. 1122, 1123,1124, 1134, 1223, 1224, 1234, 2234 Sadly though it doesn't show how to get the answer ie. which formulas used.. 
March 23rd, 2010, 08:58 AM  #6 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: Question on Combinations
{1 ,1, 2, 2, 3, 4} What if we take exactly one 1 and one 2? There is 1 choice. What if we take two 2's and up to one 1? Then we have 3 choose 1 choices. Similarly, two 1's and up to one 2? 3 choose 1 choices. Finally, what if we take exactly two 2's and two 1's? We have 1 choice. Which yields 8, and is an extension of the example I previously posted. 
March 23rd, 2010, 09:00 AM  #7 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: Question on Combinations
Perhaps I should note that it might be more natural to have enumerated those as 3 choose 2 instead of 3 choose 1, despite their equality.

March 23rd, 2010, 02:53 PM  #8 
Newbie Joined: Mar 2010 Posts: 10 Thanks: 0  Re: Question on Combinations
I see what you do there. So for these types of question do we not have a proper formula that we can use?

March 23rd, 2010, 03:27 PM  #9  
Newbie Joined: Mar 2010 Posts: 10 Thanks: 0  Re: Question on Combinations Quote:
 
March 24th, 2010, 08:14 AM  #10 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: Question on Combinations
What are you asking? I counted 1122 exactly once, in my fourth case, when I said I had two 2's and two 1's. 

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