Answer:
17
Step-by-step explanation:
Number of students in soccer club, n(S) = 50
Number of students in Art club, n(A) = 53
Number of students in Gaming club, n(G)
n([tex]S \cup A\cup G[/tex]) = 100
n([tex]S \cap A\cap G[/tex]) = 9
n([tex]S \cap A[/tex]) = 20
n([tex]A \cap G[/tex]) = 35
n([tex]G \cap S[/tex]) = 29
Formula:
n ( A ∪ B ∪ C ) = n(A) + n(B) + n(C) – n ( A ∩ B ) – n(B ∩ C) – n (A ∩ C) + n( A ∩ B ∩ C )
Putting the values:
100 = 50 + 53 + n(G) - 20 - 35 - 29 + 9
100 = 112 + n(G) - 84
n(G) = 72
Number of students in gaming club only = n(G) - n([tex]G \cap S[/tex]) - n([tex]A \cap G[/tex]) + n([tex]S \cap A\cap G[/tex])
= 72 - 35 - 29 + 9
= 17
