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Out of 450 students of a school 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
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- 50
- 100
- 75
- 225
- 50
Correct Option: B
As per the given in question , we have
Number of students who play either football or cricket or both
A → football = 450 – 50 = 400 = n(A∪B)
B → Cricket n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
⇒ 400 = 325 + 175 – n(A ∩ B)
⇒ n(A ∩ B) = 500 – 400 = 100
Hence , 400 students play both football and cricket .
