How many derangements of the set {1,2,3,4,5}\{1, 2, 3, 4, 5\}{1,2,3,4,5} are there?
444444
5!∑k=05(−1)kk!5! \sum_{k=0}^{5} \frac{(-1)^k}{k!}5!∑k=05k!(−1)k
120(12−16+124−1120)120(\frac{1}{2} - \frac{1}{6} + \frac{1}{24} - \frac{1}{120})120(21−61+241−1201)
606060