Question

In a school, 100 students were interviewed 28 took PE, 31 took BIO, 42 took ENG, 9 took PE and BIO, 10 took PE and ENG, 6 took BIO and ENG, 4 took all three subjects, then How many students took none of the three subjects?

Answer 1

To find the number of students who took none of the three subjects, we can use the principle of inclusion-exclusion.

First, let's add up the number of students who took each subject:
PE: 28 students
BIO: 31 students
ENG: 42 students

Next, let's subtract the number of students who took two subjects:
PE and BIO: 9 students
PE and ENG: 10 students
BIO and ENG: 6 students

Now, let's subtract the number of students who took all three subjects:
PE, BIO, and ENG: 4 students

To find the number of students who took none of the three subjects, we subtract the total number of students who took any of the subjects from the total number of students:

Total students - (PE + BIO + ENG - PE and BIO - PE and ENG - BIO and ENG + PE, BIO, and ENG)

100 - (28 + 31 + 42 - 9 - 10 - 6 + 4) = 100 - 90 = 10

Therefore, 10 students took none of the three subjects.