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I have n boxes and n eggs, which were hidden randomly in these boxes. The probabilty, that no egg is in the right box, is $$ \sum_{k=2}^n (-1)^k \frac{1}{k!} $$

How can I get to this formula?

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    $\begingroup$ See here $\endgroup$ – Helmut Apr 20 at 9:18
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    $\begingroup$ Such permutations are called derangements, and is a typical application of inclusion-exclusion principle. You can find an extensive list of Q&A's related to this in this community. $\endgroup$ – Sangchul Lee Apr 20 at 9:18
  • $\begingroup$ Ok thank you. I will look for that:) $\endgroup$ – Steven33 Apr 20 at 10:33
  • $\begingroup$ Maybe you can explain. why the index of the sum starts at 2? $\endgroup$ – Steven33 Apr 20 at 10:40

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