Inclusion Exclusion Application If $A$, $B$, and $C$ are finite sets then, the number of elements in EXACTLY ONE (i.e. at most one) of the sets $A$,$B$,$C$:$$n(A)+n(B)+n(C)-2 \times n(A \cap B)-2 \times n(A \cap C)-2 \times n(C \cap B) + 3 \times n(A \cap B \cap C)$$
I can derive the above through inclusion-exclusion, but would there be a general formula for $n$ finite sets?

Let A,B,C be pairwise disjoint.  Then
$n(A)+n(B)+n(C)-2 \times n(A \cap B)-2 \times n(A \cap C)-2 \times n(C \cap B) + 3 \times n(A \cap B \cap C)$
= $n(A)+n(B)+n(C)$
Pray do tell, which of A,B,C has $n(A)+n(B)+n(C)\ $ elements?
Does two of those sets have to be empty?
For example, A = {1}, B = {2}, C = {3}.
