There are 750 students in a school, and every student is enrolled in at least one class. The number of students in each class follows.
A total of 600 students are taking English.
A total of 500 students are taking math.
A total of 450 students are taking history.
A total of 400 students are taking English and math.
A total of 250 students are taking math and history.
A total of 300 students are taking history and English.
If you choose a student at random, what is the probability that they are taking math, English, and history (all three courses)?
Hint: Use the Inclusion-Exclusion Principle.
Enter your answer as a fraction in simplest terms
