Question

В классе 25 учащихся. Из них 15 изучает английский язык,12 — французский, 10 — немецкий. Все учащиеся изучают хотя бы один язык, а есть изучающие и два, и три языка. Может ли найтись ровно 3 учащихся, изучающих ровно два иностранных языка?

Answer 1

25-18=7-изучают английский
27-18=9-английский;
7+9+18=34-иностранный.
Ответ:34 изучают иностранный,9 немецкий и 7 английский

Answer 2

Analysis of Language Study

To determine if there are exactly 3 students studying exactly two foreign languages, we can analyze the given information.

Given: - Total students in the class: 25 - Students studying English: 15 - Students studying French: 12 - Students studying German: 10 - All students study at least one language, and some study two or three languages.

Solution

To find out if there are exactly 3 students studying exactly two foreign languages, we can use the principle of inclusion-exclusion.

1. First, we find the total number of students studying at least one language: - English: 15 - French: 12 - German: 10 - Total: 15 + 12 + 10 = 37 (This count includes students studying more than one language)

2. Next, we find the total number of students studying more than one language: - Students studying English and French: ? (Not directly given) - Students studying English and German: ? (Not directly given) - Students studying French and German: ? (Not directly given) - Students studying all three languages: ? (Not directly given)

3. Using the principle of inclusion-exclusion, we can find the total number of students studying more than one language.

4. Finally, we can determine if there are exactly 3 students studying exactly two foreign languages.

Conclusion

Based on the given information, we can't directly determine if there are exactly 3 students studying exactly two foreign languages. Further information about the overlap between language studies is needed to make a definitive conclusion.