In detail

The confusion of hats

The confusion of hats

There are very interesting riddles that can arise at any time between the various changes and hazards of this life.

George Washington Johnson, the honest keeper in a recent fashion show, wants to know the solution to the following problem.

At the end of the show there were only six hats left, but the applicants were so stunned that none could find the corresponding shelter, let alone recognize what their hat was. Completely desperate, Johnson was forced to allow each of them to make his own choice.

It happened that the six took a hat that did not belong to them. From the point of view of a fan of riddles, it is interesting to determine what are the chances of something like this happening.

If each of the six men chooses a hat at random, What is the probability that none of them take their own hat?

Solution

The probability that none of the six men receive their hat is 265/720.

(This result is reached as follows. The number of ways that n hats can be turned randomly without even one of the people receiving their own hat is:

n! (1 - 1/1! + 1/2! - 1/3!… + - 1 / n!)