Question

In a class of 80 students ,39 students play
football and 45 play cricket and 15
students play both the games. Then the
number of students who play neither is
O 11
O 14
O 16
O 18​

Answer 1

Given,

Total students = 80

Plays football = 29

Plays cricket = 45

Plays both = 15

To find,

Number of students that play none of the games.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Now,

Total number of cricket players = Those who only play cricket + Those who plays both games

Those who only play cricket = Total number of cricket players - Those who plays both games

Those who only play cricket = 45-15 = 30

Similarly,

Those who only play football = 39-15 = 24

Now,

Total number of students = Those who only play cricket + Those who only play football + Those who play the both + Those who play none of the games

80 = 30+24+15+ Those who play none of the games

Those who play none of the games + 69 = 80

Those who play none of the games = 80-69 = 11

Hence, 11 students play neither of the games.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

In a class of 80 students ,39 students play football and 45 play cricket and 15 students play both the games. Then the number of students who play neither is

• 11

• 14

• 16

• 18

EVALUATION

Here it is given that in a class of 80 students ,39 students play football and 45 play cricket and 15 students play both the games.

Let U = The set of all students

A = Set of students who play football

B = Set of students who play cricket

So by the given condition

n(U) = 80 , n(A) = 39 , n(B) = 45 , n(A∩B) = 15

We are aware of the formula on set theory

n(A∪B) = n(A) + n(B) - n(A∩B)

⟹ n(A∪B) = 39 + 45 - 15

⟹ n(A∪B) = 69

Hence the required number of students who play neither is

= n(A'∩B')

= n[ (A∪B)' ]

= n(U) - n(A∪B)

= 80 - 69

= 11

FINAL ANSWER

Hence the number of students who play neither is = 11

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