[tex]|\bar{B}_{1}.\bar{B}_{2}.\bar{B}_{3}...\bar{B}_{n}|=|U|-\sum |B_{i}| \sum |B_{i}.B_{j}|-...(-1)^{n}|B_{1}.B_{2}...B_{n}|=n!-\binom{n}{1}(n-1)! \binom{n}{2}(n-2)!-...(-1)^{n}\binom{n}{n}(n-n)!=\frac{n!}{0!}-\frac{n!}{1!} \frac{n!}{2!}-...-(-1)^{n}\frac{n!}{n!}=n!(\frac{1}{0!} \frac{1}{1!}-\frac{1}{2!}-...\frac{(-1)^{n}}{n!})=n!\sum_{i=0}^{n}\frac{(-1)^{i}}{i!}[/tex]