How to split and align equations when they are inside an enumerate environment?

Question

How to make the first line of aligned equations sit in the same baseline as the bullet and make the equation left justified?

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{itemize}
    \item $3!=3\times2\times1=6$
    \item $\tfrac{5!}{3!}=\tfrac{5\times4\times3!}{3!}=5\times4=20$
    \item \begin{align*}
                    \frac{n!}{(n-2)!}   &=\frac{n\times(n-1)\times(n-2)!}{(n-2)!}\\
                                                        &=n\times(n-1)\\
                                                        &=n^2-n
                \end{align*}
\end{itemize}
\end{document}

Answer 1

the aligned environment works just fine, with the [t] option to get the bullet on the first line:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{itemize}
    \item $3!=3\times2\times1=6$
    \item $\tfrac{5!}{3!}=\tfrac{5\times4\times3!}{3!}=5\times4=20$    
    \item $\!\begin{aligned}[t]
                    \frac{n!}{(n-2)!}   &=\frac{n\times(n-1)\times(n-2)!}{(n-2)!}\\
                                                        &=n\times(n-1)\\
                                                        &=n^2-n
                \end{aligned}$
\end{itemize}

\end{document}

edit: added a negative thin space \! just before the aligned block to counteract the thin space \, built into the beginning of aligned. for some background, see the question Why is there a \, space at the beginning of the “aligned” environment?.