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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. Of the 510 graduates 209 had at least one year of Spanish. 175 had at least one year of French. 149 had at least one year of German. 39 had at least one year of Spanish and French. 29 had at least one year of Spanish and German. 23 had at least one year of French and German. 8 had at least one year of all three languages. (a) How many of the graduates had at least 1 yr of at least one of the three languages? (b) How many of the graduates had at least 1 yr of exactly one of the three languages? (c) How many of the graduates had less than 1 yr of any of the three languages?
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