Bài 4: Một công ty có 100 nhân viên, biết rằng có 25 người đi học thêm tiếng Pháp , 32 người học tiếng Anh, và 37 người học thêm tiếng Nga, trong đó có 7 người học cả tiếng Anh và tiếng Pháp, 12 người...

To solve this problem, we can use the principle of inclusion-exclusion. We start by adding the number of people studying each language and then subtracting the number of people studying two languages at a time, and finally adding back the number of people studying all three languages. Let's denote: - A: the number of people studying French - B: the number of people studying English - C: the number of people studying Russian We have: A = 25 (people studying French) B = 32 (people studying English) C = 37 (people studying Russian) Now, we can calculate the number of people who study two languages at a time: AB = 7 (people studying both French and English) AC = 12 (people studying both French and Russian) BC = 16 (people studying both English and Russian) And the number of people who study all three languages: ABC = 3 To find out how many people do not study any foreign language, we use the formula: \[ \text{Total} = A + B + C - AB - AC - BC + ABC \] Substitute in the given values: \[ \text{Total} = 25 + 32 + 37 - 7 - 12 - 16 + 3 \] \[ \text{Total} = 62 \] So, there are a total of 62 employees who study at least one foreign language. To find out how many do not study any foreign language, we subtract this from the total number of employees: \[ \text{Number not studying any language} = 100 - \text{Total} \] \[ \text{Number not studying any language} = 100 - 62 \] \[ \text{Number not studying any language} = 38\] Therefore, there are $\boxed{38}$ employees who do not study any foreign language.