How does $n(n-1)(n-2)\cdots(n-m+1) \cdot \frac{(n-m)(n-m-1)\cdots1}{(n-m)(n-m-1)\cdots1} = \frac{n(n-1)(n-2)\cdots1}{(n-m)(n-m-1)\cdots1} $ I'm having issues understanding how the previous line goes to the net line.
$$
\text{Assume } m \le n \\
n(n-1)(n-2)...(n-m+1) \cdot \frac{(n-m)(n-m-1)\cdots1}{(n-m)(n-m-1)\cdots1} \\
= \frac{n(n-1)(n-2)\cdots1}{(n-m)(n-m-1)\cdots1} $$
I just don't see how the numerator of the fraction in first line cancels out yet nothing in the denominator cancels out.
Also I'm not sure what tag this question should go under.

Look at a concrete example, say $n=6$ and $m=3$. Then $n-m+1=6-3+1=4$, so we have
$$\begin{align*}
6\cdot5\cdot4&=6\cdot5\cdot4\cdot\color{brown}1\\\\
&=6\cdot5\cdot4\cdot\color{brown}{\frac{3\cdot2\cdot1}{3\cdot2\cdot1}}\\\\
&=\frac{6\cdot5\cdot4\cdot\color{brown}{3\cdot2\cdot1}}{\color{brown}{3\cdot2\cdot1}}\\\\
&=\frac{6!}{3!}\;.
\end{align*}$$
The general case is the same thing.
