Question

*Each student from a group of students plays at least one game. 55 play football, 35 play hockey, 50 play cricket, 20 play football and hockey, 15 play football and cricket, 12 play hockey and cricket and 8 play all the three games. Find the total number of students in the group.*

1️⃣ 85
2️⃣ 101
3️⃣ 100
4️⃣ 140​

Answer 1

Given : Each student from a group of students plays at least one game. 55 play football, 35 play hockey, 50 play cricket, 20 play football and hockey, 15 play football and cricket, 12 play hockey and cricket and 8 play all the three games.

To Find : the total number of students in the group.*

1️⃣ 85

2️⃣ 101

3️⃣ 100

4️⃣ 140​

Solution:

Football F = 55

Hockey  H  = 35

Cricket C  = 50

football and hockey F ∩ H = 20

football and cricket F ∩ C = 15

hockey  and cricket H ∩ C = 12

all the three games. F ∩ H ∩ C = 8

None = 0   ( students plays at least one game. )

 T = Total

T = F + H + C -  F ∩ H -  F ∩ C -  H ∩ C + F ∩ H ∩ C + None

=> T = 55 + 35 + 50 - 20 - 15 - 12  +  8 + 0

=> T = 101

total number of students in the group.* = 101

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