2.10 Fatoriais

\(n!=n.(n-1).(n-2)\dots(n-(n-1)).(n-n)\)

\(1!=1\)

\(0!=1\)

\[\begin{align*} P_{(n,n)} & = \frac{n!}{(n-n)!} = \frac{n!}{0!} = n! \\ C_{(n,0)} & = \frac{n!}{ 0! \times (n-0)! } = \frac{n!}{ 1 \times (n)!} = 1 \\ C_{(n,1)} & = \frac{n! }{ 1! (n-1)!} \\ & = \frac{ n! }{(n-1)! } \\ & = \frac{ n \times (n-1)! }{ (n-1)!} = n \end{align*}\]