Question 1042549
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One evening, n men enter the restaurant and put their hats at the reception. Each man gets a random hat back 
when going back after having dinner. Find the expected number of men who get their right hat back.
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It is a good problem and the formulation is good.


But, in order to be solved, it should be reformulated in mathematically correct form.


<pre>
In my view, this correct formulation is as follows.

Among n! permutations of "n" numbers 1, 2, 3, . . . , n how many are those where the number "k" is in the k-th place (in k-th position) ?

Then the answer is obvious: there are (n-1)! of such permutations.

And we are interested in this ratio {{{(n-1)!/n!}}}, which is equal to {{{1/n}}}.

<U>Answer</U>.  {{{1/n}}}.  Option C.
</pre>

On permutations, read the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>

in this site.