In a group of 25 students aged between 16 years and 18 years ,it was found that 15 play
cricket ,12 play tennis,11 football,5 play both cricket and football,9 play both cricket and tennis
,4 play tennis and football and 3 play all the games. Based on this answer the following
questions:
Answers
Given : a group of 25 students aged between 16 years and 18 years
15 play cricket ,12 play tennis,11 football,
5 play both cricket and football,
9 play both cricket and tennis
4 play tennis and football and
3 play all the games.
To Find : The number of students in the group who play only football is
The number of students in the group who play only cricket is
The number of students in the group who play only tennis is
The number of students in the group who play football and cricket but not tennis is
The number of students who do not play any of the three games is
Solution:
C = 15
T = 12
F = 11
C ∩ F = 5
C ∩ T = 9
F ∩ T = 4
C ∩ F ∩ T = 3
The number of students in the group who play only football is
= F - C ∩ F - F ∩ T + C ∩ F ∩ T
= 11 - 5 - 4 + 3
= 5
The number of students in the group who play only cricket is
=C - C ∩ F - C ∩ T + C ∩ F ∩ T
= 15 - 5 - 9 + 3
= 4
The number of students in the group who play football and cricket but not tennis is C ∩ F - C ∩ F ∩ T
= 5 - 3
= 2
The number of students who do not play any of the three games is
Total = C + F + T - C ∩ F - C ∩ T - T ∩ F + C ∩ F∩T + None
=> 25 = 15 + 12 + 11 - 5 - 9 - 4 +3 + None
=> 25 = 23 + None
=> None = 2
he number of students who do not play any of the three games is 2
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