A grade 12 student is selected at random to sit on a university liaison committee. Of the 129 students enrolled in the grade 12 university-preparation mathematics courses,

53 are enrolled in data management

71 are enrolled in calculus

36 are enrolled in geometry

16 are enrolled in both data management and calculus

12 are enrolled in both calculus and geometry

6 are enrolled in both geometry and data management

3 are enrolled in all three of data management, calculus, and geometry

a) Draw a Venn diagram to illustrate this situation.

b) Determine the probability that the student selected will be enrolled in either data management of calculus.

c) Determine the probability that the student selected will be enrolled in only one of the three courses.