Verified answer

I call set of students who plays fútbol : F

who likes voleibol : V

draw a rectangle , value = 560 students

Within the rectangle draw two circles , intersect them , mark F and V

Set F values 500 - 300(v) = 200 (F) plays fútbol

Set V value 500 - 320 (f) = 180 (V) plays voleibol

The intersection value : 300 - 180 = 120 (fútbol and voleibol)

Who plays both are within the intersection ,be set X :

Then 560 - 200 - 180 = 120 + X

x = 60 plays both

In a survey conducted among 560 students of a school, it was found that 320 like football game, 300 like volleyball games and 500 like at least one games.

(a) Find the number of students who like both games.

(b) Find the number of students who don't like any game.

Answers :

(a) 120 students like both games.

(b) 60 students don't like any game.

{refer to attached picture for detailed explanation}