If you have:
n!(n+1), that simplifies to (n+1)!
but how would you do that for:
(n-r)!(n-r-1)!
or
(r+1)!(r!)
Thanks in advance.
$\displaystyle \begin{gathered}
\left( {n - r} \right)!\left( {n - r - 1} \right)! = \left( {n - r} \right)\left[ {\left( {n - r - 1} \right)!} \right]^2 \hfill \\
\left( {r + 1} \right)!\left( {r!} \right) = \left( {r + 1} \right)\left( {r!} \right)^2 \hfill \\
\end{gathered} $