In a group of 200 students, each student studies 8 subjects and each subject is studied by 20 students. What is the total number of subjects:
Definitely 80
Definitely 80 is correct.
When each student takes a fixed number of subjects and each subject is taken by a fixed number of students, the total number of (student, subject) enrolments can be counted two ways, giving an equation that fixes the number of subjects.
Step 1 — Count enrolments by students: \(200\) students × \(8\) subjects each = \(1600\) enrolments.
Step 2 — Count enrolments by subjects: if \(S\) is the number of subjects, each is taken by 20 students giving \(20S\) enrolments.
Step 3 — Equate the two totals: \(20S = 1600 \Rightarrow S = 80\). The two different counts of the same quantity must agree, so there are definitely 80 subjects.
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