Three tired cowboys entered a saloon and hung their hats on a buffalo horn at the entrance. When the cowboys left deep into the night, they were unable to distinguish one hat from another and therefore picked up three hats at random. Find the probability that none of them took their own hat.
Cowboys have 6 different ways to take hats. In only two of the six options, none of the cowboys will take their own hat, because the cowboy who takes the hat first can take any of the two hats of the other cowboys. The remaining cowboys have no choice, as one of their hats is still not taken, which means he must take the other hat.

Thus, the desired probability is 2/6 $=1 / 3$.

## Answer

$1 / 3$.