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Counting Students Passing Subjects

1175BeginnerCombinatoricsCounting Principles

Brazilian Mathematical Olympiad

In a class of 70 students, we have: I) 14 boys passed Mathematics; II) 12 boys passed Physics; III) 10 boys and 16 girls failed both Mathematics and Physics; IV) 32 are boys; V) 10 passed both subjects; VI) 22 passed only Mathematics. How many girls passed only Physics?
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