Combinatorics › Combinations and selections › Choosing with gaps

Subsets with a gap pattern

High school · ●●○○○ 20 pts

Determine the number of subsets SS of {1,2,3,…,10}\{1,2,3,\ldots,10\} with the following property: there exist integers a<b<ca<b<c with a∈Sa \in S, b∉Sb \notin S, c∈Sc \in S.

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complementary countingsubsets