Answers to the Extended Problems are below in random order.
\(\begin{align}&103,776\ & \ \ &40,320\ & \ \ &1,260\\\\
&27,778\ & \ \ &2,851,368\ & \ \ &953,940\\\\
&1,728\ & \ \ &845,000\ & \ \ &362,880\\\\
&19,958,400\ & \ \ &2,500\ & \ \ &16\\\\
&247\ & \ \ &89\ & \ \ &90\\\\
&30\ & \ \ &48\end{align}\)
\(\begin{align}&103,776\ & \ \ &40,320\ & \ \ &1,260\\\\
&27,778\ & \ \ &2,851,368\ & \ \ &953,940\\\\
&1,728\ & \ \ &845,000\ & \ \ &362,880\\\\
&19,958,400\ & \ \ &2,500\ & \ \ &16\\\\
&247\ & \ \ &89\ & \ \ &90\\\\
&30\ & \ \ &48\end{align}\)