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The following is the question I am trying to solve.

There are six students each having a different gift. How many different ways can these students exchange gifts so that none of them get their own gift ?

I've tried with 1, 2 ,3 and 4 students to get 0,1,2 and 9 ways but I cannot see a pattern. Can I have some help with the general case n ?

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  • $\begingroup$ do you mean that each student has n gifts initially and at the end of the exchange? $\endgroup$
    – Akshara
    Dec 3, 2013 at 9:28
  • $\begingroup$ I've actually figured it out. It was about derangements. Thank you though. $\endgroup$
    – hyg17
    Dec 3, 2013 at 17:44

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