Answer
$420$
Work Step by Step
We are arranging letters, so order is important. Permutations.
not all of the $n=7$ letters are distinct:
There are
2 T's,
3 O's
1 R and
1 N
We use the Permutations of Duplicate Items formula:
The number of permutations of $n$ items, where
$p$ items are identical,
$q$ items are identical,
$r$ items are identical, and so on, is $\displaystyle \frac{n!}{p!q!r!\ldots}$
$\displaystyle \frac{7!}{2!3!1!1!}=\frac{7\times[6]\times 5\times 4\times(3\times 2\times 1)}{[2]\times 1\times(3\times 2\times 1)\times 1\times 1}$
... after reducing
$=7\times 3\times 5\times 4$
$=420$
