# Mean Number of Elements Fixed by Self-Map/Examples/7

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## Example of Mean Number of Elements Fixed by Self-Map

$7$ letters are placed at random into $7$ addressed envelopes, not necessarily making sure that one envelope contains only one letter.

How many letters, on average, can be expected to be in its correct envelope?

## Proof

This is an instance of Mean Number of Elements Fixed by Self-Map.

Hence we can expect, on average, $1$ letter to be in its correct envelope.

$\blacksquare$

## Sources

- 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): The misaddressed letters: $131$