4. Monsters and Hats III
Setup
10 people leave their labeled hats on a table.
The hats are returned randomly, without checking names.
Rules
- Each hat is equally likely to go to any person
- A person is "matched" if they receive their own hat
Question
What is the probability that at least one person is matched?
Answer format
Enter a number rounded to 2 decimal places.
Your Answer
Need help?
Hint 1
This is related to the concept of derangements - permutations where no element appears in its original position.
Hint 2
What is the probability that NO monster gets their own hat (a complete derangement)?
Hint 3
Use inclusion-exclusion or the derangement formula: D(n) = n! * sum from k=0 to n of (-1)^k / k!