Answer:
There are 3 black convertible Porsches.
Step-by-step explanation:
Venn Diagram Formula for 3 Sets:
[tex]\boxed{n(S)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)}[/tex]
Let:
A = Porsche cars
B = Black cars
C = Convertible cars
Given:
n(S) = 50
n(A) = 18
n(B) = 25
n(C) = 16
n(B∩C) = 3
n(A∩B) = 4
n(A∩C) = 5
[tex]n(S)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)[/tex]
[tex]50 = 18 + 25 + 16 - 4 - 3 - 5+n(A\cap B\cap C)[/tex]
[tex]50=47+n(A\cap B\cap C)[/tex]
[tex]\bf n(A\cap B\cap C)=3[/tex]
Therefore, there are 3 black convertible Porsches.
