Number of Derangements on Finite Set/Examples

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Examples of Number of Derangements on Finite Set

Example: $7$ Envelopes

A correspondent writes $7$ letters and addresses $7$ envelopes, one for each letter.

In how many ways can all the letters be placed in the wrong envelopes?


Example: $10$ Envelopes

A correspondent writes $10$ letters and addresses $10$ envelopes, one for each letter.

In how many ways can all the letters be placed in the wrong envelopes?