Let A, B, and C be any three events defined on a sample space S. Let
N
(
A
)
,
N
(
B
)
,
N
(
C
)
,
N
(
A
∩
B
)
,
N
(
A
∩
C
)
,
N
(
B
∩
C
)
,
and
N
(
A
∩
B
∩
C
)
denote the numbers of outcomes in all the different intersections in which A, B, and C are involved. Use a Venn diagram to suggest a formula for
N
(
A
∪
B
∪
C
)
. [Hint: Start with the sum
N
(
A
)
+
N
(
B
)
+
N
(
C
)
and use the Venn diagram to identify the “adjustments” that need to be made to that sum before it can equal
N
(
A
∪
B
∪
C
)
.] As a precedent, note that
N
(
A
∪
B
)
=
N
(
A
)
+
N
(
B
)
−
N
(
A
∩
B
)
. There, in the case of two events, subtracting
N
(
A
∩
B
)
is the “adjustment.”