Question

In one
class 18 Students play Basketball,
14Studentes play soccer and 10 studentes
play valleyball. 5 Students play
Soccer and volleyball, 7 studentes play
basketball and Valleyball and 10 Students
play-basketball and soccer. 4 students
play, all three sports. How many
students is in the clapp if every
student plays at least one
sport?​

Answer 1

Answer:

Total students in class=24

Step-by-step explanation:

n(b)=18

n(s)=14

n(v)=10

n(s int v)=5

n(b int v)=7

n(b int s)=10

n(b int v int s)=4

n(only s int v)=5-4=1

n(only b int v)=7-4=3

n(only b int s)=10-4=6

n(only s)=14-1-6-4=3

n(only b)=18-3-6-4=5

n(only v)=10-1-3-4=2

n(U)=n(b int v int s)+n(only s int v)+n(only b int v)+n(only b int s)+n(only s)+n(only b)+n(only v)=4+1+3+6+3+5+2=24

an alternative way to solve is to use Venn diagram

Answer 2

Given : every student plays at least one sport

To Find :  How many students are in the class

Solution:

every student plays at least one sport

Hence total Students = n ( B ∩ S ∩ V)

n(B) = 18

n( S) = 14

n ( V) = 10

n ( S ∩ V) = 5

n ( B ∩ V) = 7

n ( S ∩ B) = 10

n ( S ∩ V ∩ B) = 4

n ( B ∩ S ∩ V) = n(B) + n(S) + n(V) - n ( S ∩ V) - n ( B ∩ V)   - n ( S ∩ B) +  n ( S ∩ V ∩ B)

= 18 + 14 + 10 - 5 - 7 - 10 + 4

= 46 - 22

= 24

total Students = 24

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