Inspired by Paul Fournier

Two letters can be chosen out of 7 in $\begin{pmatrix}7\\2\end{pmatrix}$ ways.

Once two letters have been chosen and placed in their correct places the remaining 5 letters can be deranged in !5 ways.

Combining these two observations and using a very neat formula for the number of derangements of n objects gives

$\begin{pmatrix}7\\2\end{pmatrix}\left[\frac{5!}{e}\right]=21\times44=\boxed{924}$ .

Notes

A 'derangement' is an arrangement of objects so that no object is left in its original position.

$!n$ is the 'sub factorial of n' and is the symbol for the number of derangements of n.

The 'neat formula' states that the number of derangements of n objects is given by

$!n=\left[\frac{n!}{e}\right]$

where $[.]$ is the nearest integer function. I think the formula, or at least its precursor, can be traced back to Euler.