What is the number of non-empty subsets from the set $ (1,2,3,...,12)$ and such that the sum of the least element and the greatest element in the set is equal to $13$
the number of non-empty subsets
2
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combinatorics
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0What have you tried already? Maybe you could work out what happens in the cases when your set is {6,7} or {5,6,7,8}. – 2012-09-21
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0In standard usage one uses curly braces for _sets_ and round brackets for _tuples_; thus $\{1,2,3,\ldots,12\}$ is a set and $(1,2,3,\ldots,12)$. A set does not become a different set if one lists the members in a different order or lists one of them more than once, but a tuple becomes a different tuple if one does that; that is the difference. – 2012-09-21