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In a college, out of 850 students, 230 play cricket; 250 hockey, and 360 basketball. Of the total, if 75 play both basketball and hockey; 68 play cricket and basketball; 37 play cricket and hockey; and 30 play all three games, how many students don't play any games at all?

In a college, out of 850 students, 230 play cricket; 250 hockey, and 360 basketball. Of the total, if 75 play both basketball and hockey; 68 play cricket and basketball; 37 play cricket and hockey; and 30 play all three games, how many students don't play any games at all? Correct Answer 160

Formula used:

If A, B, and C are finite sets, then

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C)

n(A ∪ B ∪ C) = Number of students play at least one game

Calculation:

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According to the question

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(A ∩ C) + n(A ∩ B ∩ C)

⇒ 230 + 360 + 250 - 68 - 75 - 37 + 30

⇒ 870 - 180 = 690 

Number of students who don't play any games = 850 - 690

⇒ 160

∴ The number of students who don't play any games is 160.

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