5. In a certain primary school, 94 students are in the sixth grade. Some students are involved in extracurricular activities: English and German language classes, and sports clubs. Extracurricular English is attended by 40 students, German by 27 students, and sports activities by 60 students. Of the students involved in sports activities, 24 also attend English classes. Ten students who attend English classes also attend German classes. Twelve students who attend German classes are also involved in sports activities. Four students are involved in all three extracurricular activities. How many students are involved in only one of these extracurricular activities, and how many are not involved in any of them?

Each problem is worth 10 points.

The use of a pocket calculator or any reference materials is not allowed.
First method:

A total of 40 students go to English class. Of these 40, 24 students are also involved in some sports activity, 10 students go to German language class, and 4 students are involved in all three activities.

Only English is studied by $40-24-10+4=10$ students.

By analogous reasoning, we arrive at the number of students involved in

- only German: $27-12-10+4=9$,

2 POINTS

- only sports activities: $60-24-12+4=28$.

Only one activity is pursued by $10+9+28=47$ students.

1 POINT

Some of these activities are pursued by

$40+28+9+(12-4)=40+28+9+8=85$ students.

2 POINTS

None of these activities are pursued by

$94-(40+9+28+8)=94-85=9$ students.

1 POINT

TOTAL 10 POINTS