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March 21st, 2010, 05:24 AM   #1
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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.
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March 21st, 2010, 05:04 PM   #2
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Re: Question on Combinations

What is a multiset combination?
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March 21st, 2010, 06:10 PM   #3
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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.
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March 22nd, 2010, 01:22 PM   #4
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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.
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March 23rd, 2010, 06:39 AM   #5
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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..
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March 23rd, 2010, 08:58 AM   #6
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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.
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March 23rd, 2010, 09:00 AM   #7
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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.
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March 23rd, 2010, 02:53 PM   #8
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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?
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March 23rd, 2010, 03:27 PM   #9
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Re: Question on Combinations

Quote:
Originally Posted by jason.spade
{1 ,1, 2, 2, 3, 4}

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.

Which yields 8, and is an extension of the example I previously posted.
won't they give repeat of 1122?
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March 24th, 2010, 08:14 AM   #10
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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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