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

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: $131$