Question

3
There are 240 students in class XI 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 atleast one of the three games. How many students play all the three games?
​

Answer 1

25 member play the game

Answer 2

Answer:

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