In a class, 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics an Mathematics. If 6 students offered all the three subjects, find:
a. The total number of students.
b. How many took Maths but not Chemistry.
c. How many took exactly one of the three subjects.