Discussion
In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is ____
Answer: C
The group has 24 students.
Those who like at least one subject number, by inclusion and exclusion,
\[ n(M \cup E) = 10 + 12 - 4 = 18 \]
Adding the 6 who like neither gives \(18 + 6 = 24\).
18 forgets the 6 students who like neither subject. 20 adds 10 and 12 but forgets both corrections, and 32 adds every number in the question, counting the 4 students who like both twice and treating them as a separate group.
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