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In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English not German?

In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English not German? Correct Answer 18

Given:

Number of students who enrolled at least one of the two subjects, n(E ∪ G) = 40 

No of students enrolled in English and German both, n(E ∩ G) = 12

No of students enrolled for German, n(G) = 22 

Formula used:

n(E ∪ G) = n(G) + n(E) - n(E ∩ G)

Calculation:

Let the number of students who enrolled for only English = n(E) 

40 = 22 + n(E) - 12 

⇒ n(E) = 40 + 12 - 22 

⇒ n(E) = 30

∴ Students who enrolled for only English not German are (30 - 12) = 18 

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