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Question: problem 7 20 pts let n en be a natural...

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Problem 7. (20 pts) Let n EN be a natural nmber and X a finite set with n elements. Show that the number of permutations of X such that no element stays in the same position is n! k! k o For instance, there are 6 = 3! permutations of 3 elements, but only 2 of them are permutations which fix no element. Similarly, there are 24-4! permutations of 4 elements, but only 9 which fix no element. Hint: Use the Inclusion-Exclusion Principle, with the ith set being the set of permuta- tions which fir the ith element of x
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