Math Problem Statement
There are a total of 117 foreign language students in a high school where they offer Spanish, French and German. There are 29 students that take at least 2 languages at once. If there are 50 Spanish students, 42 French students and 50 German students, how many students take all three languages at once?
Solution
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Math Problem Analysis
Mathematical Concepts
Set Theory
Principle of Inclusion-Exclusion
Formulas
|S ∪ F ∪ G| = |S| + |F| + |G| - |S ∩ F| - |F ∩ G| - |G ∩ S| + |S ∩ F ∩ G|
Theorems
Inclusion-Exclusion Principle
Suitable Grade Level
Grades 10-12
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