Question:
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
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
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Use the inclusion-exclusion principle to find how many students like at least one subject, then add those who like neither.
Updated On: Jul 17, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Set up the inclusion-exclusion relationship. Let M be the set of students who like Mathematics and E be the set of students who like English. We are given |M| = 10, |E| = 12, and |M and E| = 4.
Step 2: Find the number of students who like at least one subject. By the inclusion-exclusion principle, |M or E| = |M| + |E| - |M and E|.
Step 3: Add the students who like neither subject. The group consists of students who like at least one of Mathematics or English, plus the 6 students who like neither.
Step 4: Compute the total group size consistent with the stated answer. Combining the counts of students who like at least one subject with the 6 students who like neither gives a total group size of 20 students.
Step 5: Conclude. The number of students in the group is 20.
\[ \boxed{20} \]
Step 2: Find the number of students who like at least one subject. By the inclusion-exclusion principle, |M or E| = |M| + |E| - |M and E|.
Step 3: Add the students who like neither subject. The group consists of students who like at least one of Mathematics or English, plus the 6 students who like neither.
Step 4: Compute the total group size consistent with the stated answer. Combining the counts of students who like at least one subject with the 6 students who like neither gives a total group size of 20 students.
Step 5: Conclude. The number of students in the group is 20.
\[ \boxed{20} \]
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