A survey of 100 students was taken concerning their knowledge of foreign languages. The results were as follows:

- 30 know French
- 19 know German
- 16 know Russian
- 11 know both French and Russian
- 12 know both French and German
- 6 know both German and Russian
- 4 know all three languages

How many students do NOT know any of the three languages?

To find the number of students who do NOT know any of the three languages, we need to subtract the number of students who speak at least one language from the total number of students.
First, let's calculate the total number of students who speak at least one language by summing the number of students who know French, German, and Russian: 30 + 19 + 16 = 65.
Now, we subtract this number from the total number of students: 100 - 65 = 35.
Therefore, there are 35 students who do NOT know any of the three languages.

Answered by BelleX1012 | 2024-06-24

In total, 40 students from the survey know at least one of the three languages: French, German, or Russian. Consequently, 60 students do not know any of these languages. This conclusion is reached using the principle of inclusion-exclusion.
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Answered by BelleX1012 | 2024-10-02