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Q28 (CAPF/2024) Miscellaneous & General Knowledge › Sports, Games & Awards › Sports, Games & Awards

Out of a class of 100 students, 25 play at least cricket and football, 15 play at least cricket and hockey, 12 play at least football and hockey and 10 play all the three sports. The number of students playing cricket, football and hockey are 50, 37 and 22, respectively. The number of students who do NOT play any of the three sports is

Result
Your answer: —  ·  Correct: A

Explanation

To find the number of students who do not play any sport, we use the Inclusion-Exclusion Principle for three sets:

n(C ∪ F ∪ H) = n(C) + n(F) + n(H) - [n(C ∩ F) + n(C ∩ H) + n(F ∩ H)] + n(C ∩ F ∩ H)

  • n(C) = 50
  • n(F) = 37
  • n(H) = 22
  • n(C ∩ F) = 25
  • n(C ∩ H) = 15
  • n(F ∩ H) = 12
  • n(C ∩ F ∩ H) = 10

Calculation:
Total playing at least one sport = 50 + 37 + 22 - (25 + 15 + 12) + 10
Total = 109 - 52 + 10 = 67

Students who do NOT play any sport = Total class size - Total playing
100 - 67 = 33

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