Hats and People
7 people walk into a room and place their respective hats on a table. When they walk out, the light suddenly goes off, but they are in a hurry and have to leave immediately. Therefore, they all pick a random hat from the table and walk out. What is the probability that none of them pick up their own hat from the table?
Give your answer as a decimal rounded to 2 decimal points .
The answer is 0.37.
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1 solution
Relevant wiki: Derangements
This problem uses derangements [ Derangements Wikipedia ]. The sub-factorial of 7 is: !7=1854. There are 7!= 5040 possible arrangements of the people picking hats. Therefore, the probability of no one picking up their own hat is !7/7!≈ 0.37 ( 2 decimal places).