Question

Решить задачу. Из 35 студентов сдали зачеты по английскому языку 14 человек, по русскому языку – 12 человек, по литературе- 16 человек. Трое студентов сдали английский язык и русский; английский и литературу сдали 3 студентов; литературу и русский- 4 чел. Сколько студентов сдали зачеты по всем трем предметам?

Answer 1

14+16+12-36=7
по всем предметам не более трёх человек
литра на 1 больше, чем англ. яз 7-1=6
литра=русс=2+2
6-4=2
2-1=1
1
 

Answer 2

Problem Analysis

We are given the number of students who passed exams in English, Russian, and Literature, as well as the number of students who passed exams in combinations of these subjects. We need to determine the number of students who passed exams in all three subjects.

Solution

To solve this problem, we can use the principle of inclusion-exclusion. We will start by adding the number of students who passed exams in each subject individually. Then, we will subtract the number of students who passed exams in combinations of two subjects. Finally, we will add back the number of students who passed exams in all three subjects.

Let's calculate the number of students who passed exams in all three subjects step by step:

1. Number of students who passed the English exam: 14. 2. Number of students who passed the Russian exam: 12. 3. Number of students who passed the Literature exam: 16. 4. Number of students who passed both English and Russian exams: 3. 5. Number of students who passed both English and Literature exams: 3. 6. Number of students who passed both Russian and Literature exams: 4.

Now, let's calculate the number of students who passed exams in all three subjects using the inclusion-exclusion principle:

Number of students who passed exams in all three subjects = Number of students who passed the English exam + Number of students who passed the Russian exam + Number of students who passed the Literature exam - Number of students who passed both English and Russian exams - Number of students who passed both English and Literature exams - Number of students who passed both Russian and Literature exams + Number of students who passed exams in all three subjects.

Number of students who passed exams in all three subjects = 14 + 12 + 16 - 3 - 3 - 4 + Number of students who passed exams in all three subjects.

Let's solve this equation to find the number of students who passed exams in all three subjects:

Number of students who passed exams in all three subjects = 14 + 12 + 16 - 3 - 3 - 4 = 32.

Therefore, 32 students passed exams in all three subjects.

Answer

The number of students who passed exams in all three subjects is 32.