transformation of an equation (Binomial coefficient)

Question

Good afternoon

I don't understand this transformation. Can you please help me?

Greetings

Ava

$\begin{align}{n \choose k}&=\frac{n}{1}\cdot\frac{n-1}{2}\cdots\frac{n-(k-1)}{k}\\&=\frac{n\cdot (n-1)\cdots(n-k+1)}{k!}\end{align}$

Answer 1

By definition $$\binom{n}{k}=\frac{n!}{k!(n-k)!}=\frac{n(n-1)\ldots(n-k+1)(n-k)!}{k!(n-k)!}$$

Cancel out the$ (n-k)!$ and you're done.