Answer
The number of ways of forming a four-letter password is $840$.
Work Step by Step
We know that:
${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$
So, from the information,
$\begin{align}
& n=7 \\
& r=4 \\
\end{align}$
Then, we have to find the number of permutations of 7 things taken 4 at a time:
$\begin{align}
& {}_{7}{{P}_{4}}=\frac{7!}{\left( 7-4 \right)!} \\
& =\frac{7!}{3!} \\
& =\frac{7\times 6\times \ldots \times 3!}{3!} \\
& =840
\end{align}$
Thus, the number of ways of forming a four-letter password is $840$.
