Observe the given figure and answer question below:

If 50 play football, 40 play cricket and 30 play basketball, then what is the number of players who play football or cricket but not basketball?

The shaded part represents is the number of players who play football or cricket but not basketball.

 n(A∪B) = n(A) + n(B) - n(A⋂B)

The number of players who play football or cricket but NOT basketball = Number of player who play cricket and football – (Number of player who play both basketball and cricket + Number of player who play both Basketball and football + Number of player who play Basketball, Cricket and football)

And

Number of player who play cricket and football = The number of players who play football + The number of players who play cricket - The number of players who play both football and cricket

Number of player who play cricket and football = 50 + 40 - (14 + 5) = 71

So,

The number of players who play football or cricket but not basketball =

= 71 – (9 + 7 + 5)

= 71 – 21

= 50

Hence, ‘50’ number of players who play football or cricket but NOT basketball.

Additional Information

Players who play only Football = 50 - (14 + 7 + 5) = 24

Players who play only Cricket= 40 - (14 + 9 + 5) = 12

Players who play only Basketball = 30 - (9 + 7 + 5) = 9