THIS IS COMPLETE QUESTION PLEASE SOLVE WITH WHATEVER YOU HAVE

1. Find a RR for the number of derangements, Dn, of n numbers. A derangement is a permutation of 1,2,3,...,n where no element is at its original place. So D2 = 1 since 2,1 is the only derangement of 1,2. Hint: One way to find the RR is to use the inclusion-exclusion principle for some small n. See also internet for good explanations. For example use the sum rule. Say number 1 and 2 are shifted, how many derangements then? If 1 is not allowed on position 2, how many derangements then? Solve it with RSolve and plot the first few Dn. Since Mathematica wants to be exact real initial values is a good idea.