In a class of 30 students, 18 play cricket, 12 play football, and 5 play both. How many students play at least one of the two games?
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Answer and explanation
Correct answer: 25
‘At least one game’ means the union of the cricket and football groups. By inclusion–exclusion, n(C ∪ F) = n(C) + n(F) − n(C ∩ F) = 18 + 12 − 5 = 25. The five students who play both are subtracted once because they were counted in both groups. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
‘At least one game’ means the union of the cricket and football groups. By inclusion–exclusion, n(C ∪ F) = n(C) + n(F) − n(C ∩ F) = 18 + 12 − 5 = 25. The five students who play both are subtracted once because they were counted in both groups. Hence, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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