Question

In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the total number of students in the group (Assume that each student in the group plays at least one game).​

Answer 1

Answer:

100 Students

Step-by-step explanation:

First write down all the data (this makes it easier )

Total number of students = ?

Students who play football = 65

Students who play hockey = 45

Students who play cricket = 42

Students who play football and hockey = 20

Students who play football and cricket = 25

Students who play hockey and cricket = 15

Students who play all three games = 8

Now let's start working

Students who play football and hockey = 20 - 8 = 12

Students who play football and cricket = 25 - 8 = 17

Students who play hockey and cricket = 15 - 8 = 7

Students who only play football = 65 - ( 17 + 8 + 12) = 28

Students who only play cricket = 42 - (17 + 7 + 8) = 10

Students who only play hockey = 45 - (12 + 8 + 7) = 18

Students who play all three games = 8

Now just add all these values up

TOTAL NUMBER OF STUDENTS = 12 + 17 + 7 + 28 + 10 + 18 + 8

= 100 students

Answer 2

The total number of students in the group would be:

- 100 students

Given that,

Number of students playing football = 65

Number of students playing hockey = 45

Number of students playing Cricket = 42

Number of students playing football and hockey = 20

Number of students playing football and cricket = 25

Number of students playing hockey and cricket = 15

Number of students playing all games = 8

Now,

The total number of the entire students in the group $= 65+45 + 42 - 20 - 25 - 15 + 8 = 100$  

 ∵ Total number of students $= 12 + 17 + 7 + 28 + 10 + 18 + 8$

$= 100 students$

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