Question

In one class 18 students play basketball, 14 students play soccer and 10 students play volleyball. 5 students play soccer and volleyball, 7 students play basketball and volleyball and 10 students play basketball and soccer. 4 students play all three sports. How many students are in the class if every student plays at least one sport?​

Answer 1

Answer:

24

Step-by-step explanation:

Draw A 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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