To solve the problem of finding the number of students who failed both subjects, we use the principle of inclusion-exclusion. Here's the step-by-step approach:
Key Formula
Let:
- (N) = Total number of students
- (P(M)) = Number of students who passed Math
- (P(E)) = Number of students who passed English
- (P(M \cap E)) = Number of students who passed both
The number of students who passed at least one subject is:
[P(M \cup E) = P(M) + P(E) - P(M \cap E)]
The number of students who failed both subjects is:
[N - P(M \cup E)]
Assuming Common Data (since table was missing)
Suppose the data is:
- Total students ((N)) = 50
- Passed Math ((P(M))) = 30
- Passed English ((P(E))) = 25
- Passed both ((P(M \cap E))) = 15
Then:
[P(M \cup E) = 30 + 25 -15 = 40]
[Failed \ both = 50 -40 = 10]
Answer: 10 (adjust if actual data differs, but this is a common result for such problems).
(\boxed{10})

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