Explanation

To determine how many students like all three subjects, we can use the principle of inclusion-exclusion.

Given:

- Total number of students in the class: 30

- Number of students who like Math: 16

- Number of students who like Physics: 10

- Number of students who like English: 12

- Number of students who like Math and English: 4

- Number of students who like Physics and English: 3

- Number of students who like Math and Physics: 3

First, let's find the number of students who like at least one subject. '

To do this, we add the number of students who like each subject individually:

16 (Math) + 10 (Physics) + 12 (English) = 38

To account for this, we need to subtract the number of students who like two subjects, as we have counted them twice:

4 (Math and English) + 3 (Physics and English) + 3 (Math and Physics) = 10

Now, we have counted all the students who like at least one subject, but we need to consider the student who likes no subject.

This student is not counted in the above calculations, so we subtract 1 from the total.

38 - 10 - 1 = 27

Therefore, 27 students like at least one subject.

To find the number of students who like all three subjects

30 - 27 = 3