In this question you will demonstrate how to use the Principle of Inclusion/Exclusion to count derangements of the set {1, 2, 3, 4}. a. First, write out all 24 permutations of the set {1, 2, 3, 4}. Systematically, i.e. element by element, cross out the permutations that are not derangements and keep track of how many times you cross out each permutation. b. Second, use combinatorics and P.I.E. to calculate/count the number of derangements. (i.e. Count all permutations and then correct for all non-derangements.) c. Explain how each term of the calculation in part b) relates to the manual count done in part a)