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Similar to the hatcheck problem, suppose that everyone’s quiz, once it is graded, is returned at...

Similar to the hatcheck problem, suppose that everyone’s quiz, once it is graded, is returned at random to one of the 18
students. What is the probability no one gets their own exam back?

math   Statistics-And-Probability   
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Answer #1

total number of ways to divide 18 exam papers to 18 people =18!

number of ways none receive their exam =18!*(1-1/1!+1/2!-1/3!+1/4!-..........1/18!)

therefore probability no one gets their own exam back =(18!*(1-1/1!+1/2!-1/3!+1/4!-..........1/18!))/18!

=1-1/1!+1/2!-1/3!+1/4!-..........1/18!

=0.367879

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