Derangements. Given n letters and n addressed envelopes, in how many ways can the letters be placed in the envelopes so that no letter is in the correct envelope? Discussion. The total number of ways of putting the letters in the envelopes is the number of permutations of n objects, which is n!. We will see that the fraction of these which are incorrectly addressed is very close to 1/e, where e = 2, 71828 . . . is the base of natural logarithms—a surprising result at first sight. In fact, the exact number of ways of mis-addressing letters is the nearest integer to n!/e. Exercise: For n = 3, 4, 5, calculate the number of ways of putting n letters in the envelopes so that every letter is incorrectly addressed. Calculate the ratio of this number to n! in each case. Please explain this in detail and simpler way and show me the steps of solving the exercise

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Topological Sort

Topological sort is a sorting technique that sets up a hierarchy in a process. In this technique, when a directed network has nodes connected by arrows, the root node is placed before the successor node.