## Identifying the comination type [closed]

I have the following sequence of numbers,

3 4 5 6 7 8 9 10

I am allowed to choose say any 6 numbers from the above combination, I get

5 6 7 8 9 10
3 4 7 8 9 10
3 4 5 6 9 10
3 4 5 6 7 8


Thus the number of combinations where the order doesn't matter is only 4. Changing the order in the above combination, isn't allowed. For example,

6 5 7 9 8 10

is not allowed as it is already covered by,

5 6 7 8 9 10

But nCr(8,6)=28 will cover all such ordering I think. What type of combination am I looking at?. Is there any formula that would help find just these combinations(4 in the aove example) above?. Is there some derivative of nCr that I can use?

Any help would be most welcome. Thanks.

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Your question is not clear at all. What is special about your combinations that distinguishes them from 3 5 6 7 8 9, for instance? – darij grinberg Sep 3 2011 at 15:23