Number of Derangements on Finite Set/Mistake

Source Work

1992: David Wells: Curious and Interesting Puzzles:

The Puzzles:

The misaddressed letters

$130$

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.

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The misaddressed letters: $130$