Question

There are 240 students in class 12 of a school.,130 play cricket , 100 play football ,75 play volleyball ,30 of these play cricket and football ,25 play volleyball and Cricket,15 play football and volleyball. Also each student plays at least one of the three games. How many students play all the three games.

Answer 1

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Answer 2

Answer:

Students who plays all three games = 5

Step-by-step explanation:

Let C, F, V denote the set of students who play cricket, football and volleyball respectively

Then we have, n(U) = n(C ∪ F ∪ V) = 240,

n(C) = 130, n(F) = 100, n(V) = 75,

n(C ∩ F) = 30, n(C ∩ V) = 25, n(F ∩ V) = 15

So, students who plays all three games = n(C ∩ F ∩ V)

⇒ n(C ∩ F ∩ V) = n(C ∪ F ∪ V) - n(C) - n(F) - n(V) + n(C ∩ F) + n(C ∩ V) + n(F ∩ V)

                           = 240 - 130 - 100 - 75 + 30 + 25 + 15

                           = 5

Hence, Students who plays all three games = 5