SOLUTION: The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduat

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Question 445297: The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. The following are statements of the 520 graduates.
202 had at least one year of Spanish.
176 had at least one year of French.
143 had at least one year of German.
44 had at least one year of Spanish and French.
27 had at least one year of Spanish and German.
24 had at least one year of French and German.
5 had at least one year of all three languages.
Evaluate each of the following.
(a) How many of the graduates had at least one year of at least one of the three languages?
Answer by rfer(16322) About Me  (Show Source):