Algebra - Probability

Question

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

Answer 1

The probability is

=(600/750)*(500/750)*(450/750)=8/25

or

 

= (400/750)*(450/750)=8.25.

 

I think you can figure out why?