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 100 students in the school. There are 24 students in the Spanish class, 21 in the French class, and 12 in the German class. There are 8 in both Spanish and French, 7 in both Spanish and German, and 6 that are in both French and German. There are 2 students taking all 3 classes.


Required:

a. If a student is chosen randomly, what is the probability that they are not in any of these classes?

b. If a student is chosen randomly, what is the probability that they are taking exactly one language class/

c. If 2 students are chosen randomly, what is the probability that at least one is taking a language class?