Probability question of CLRS

Question

In a restaurant each of $n$ customer gives a hat to the hat check person. The hat check person gives the hat back to the customer in a random order. What is expected number of customer who get back their own hat?

Comments

@Satbir , 

Then out of n! cases there is only 1 correct way of giving the hat back to the customers so probability = 1/n!

What is it that you're calculating? Is it the probability to give everyone their correct hat?

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Yes.

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i thought you are just considering only that case where a single customer among various customers should get  their hat back.

Answer 1

X :  1       1        1         1           1        .......... 1  (Till n terms)

fx : 1/n   1/n     1/n      1/n        1/n                1/n       (probability that he gets the correct hat back out of n hats)

Now, expectation (or in other words mean)= x * $f_x$

= n* (1/n)

= 1.