\problemdata      
        {?} % latex-friendly label for the prob.
        {Counting} % The topic(s) of the problem content.
        {?} % Source (if known)
        {F01, TU8} % Usage (list ones you are aware of).
        {Christos Kapoutsis, S02} % Last revision info (author, date).

\begin{problem}
State the Principle of Inclusion-Exclusion for the case of three
sets $A_1,A_2,A_3$ (without looking it up first, if possible).

\solution{
$\card{A_1 \union A_2 \union A_3} =  \card{A_1} + \card{A_2} + \card{A_3} -
\card{A_1 \intersect A_2} - \card{A_1 \intersect A_3} - \card{A_2
\intersect A_3} + \card{A_1 \intersect A_2 \intersect A_3}$.
}

\end{problem}