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In a group of 100 students, each student offers exactly 8 subjects, and exactly 10 students take each subject. Find the total number of different subjects.
  • a)
    Exactly 80
  • b)
    May be 50
  • c)
    At most 30
  • d)
    At least 90
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a group of 100 students, each student offers exactly 8 subjects, an...
Step 1 — Count student–subject pairs: each of the 100 students offers 8 subjects, so total pairs = 100 × 8 = 800.
Step 2 — Relate to subjects: each subject is taken by 10 students, so if S is the number of subjects, total pairs = 10 × S.
Step 3 — Equate and solve: 10 × S = 800, hence S = 800 ÷ 10 = 80.
Answer: a) Exactly 80
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