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Three Clubs Inclusion-Exclusion Counting

1050BeginnerCombinatoricsCounting Principles

Регионален натпревар по математика за основно образование

The students of grade IVª are members of the ecology, literature, or mathematics club. Five students are members of all three clubs, and nine students are members of exactly two clubs. Eight students are members of both the ecology and literature clubs, and the same number are members of both the literature and mathematics clubs. Also, 20 students are members of exactly one club, with 5 in each of the ecology and mathematics clubs. How many students are in grade IVª?
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