Number of Derangements on Finite Set/Mistake

Source Work

 * The Puzzles:
 * The misaddressed letters
 * $130$
 * $130$

Mistake

 * A correspondent writes ten letters and addresses ten envelopes, one for each letter. In how many ways can all the letters be placed in the wrong envelopes?

The solution given is:
 * Bernoulli posed the problem in terms of $n$ letters wrongly placed into $n$ envelopes, but the principle is the same. ...
 * When $n = 7$, the value is $1854$.

Correction
The question was asked of $10$ envelopes, but the answer was given of $7$ envelopes.