Answer to Question #27248 in Combinatorics | Number Theory for Jeeg

Question

An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 96 students in the school. There are 37 in the Spanish class, 31 in the French class, and 22 in the German class. There are 14 students that in both Spanish and French, 5 are in both Spanish and German, and 8 are in both French and German. In addition, there are 2 students taking all 3 classes. If two students are chosen randomly, what is the probability that at least one of them is taking a language class?