My Math Forum Question on Combinations

 March 21st, 2010, 04:24 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, 04:04 PM #2 Senior Member   Joined: Apr 2008 Posts: 435 Thanks: 0 Re: Question on Combinations What is a multiset combination?
 March 21st, 2010, 05:10 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, 12:22 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, 05:39 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, 07:58 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, 08:00 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, 01:53 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, 02:27 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?

 March 24th, 2010, 07:14 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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