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I am struggling with the following puzzle.

Six people, on their way out from a restaurant, waiting to collect their hats. The attendant mixes up the tags and hands the hats over randomly. What are the chances that at least one of them gets the right hat?

I tried to find the probability of no one getting his hat. I reconfigured the problem as follows: each of them picks a hat, one by one, from the hat pool, without looking at the pool.

First I tried to calculate the following probabilities. However, I am not able to go beyond the first person. In the case of the second person, I have two cases 1. #1 chose his hat, and 2. his hat is still in the pool.

I am not sure how to find his probability.

P (1st not getting his hat) = 5/6

P(2nd not getting his hat ) =

P(3rd not getting his hat ) =

….

How should I go about this problem?

Thanks.

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# Hat puzzle

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