A derangement of the numbers 1 through n is a permutation of all n those numbers such that none of them is in the “right place.” For example, 34251 is a derangement of 1 through 5, but 24351 is not because 3 is in the 3rd position. We will use simulation to estimate the number of derangements of the numbers 1 through 12.
a. Write a program that generates random permutations of the integers 1, 2,…, 12. Your program should determine whether or not each permutation is a derangement.
b. Based on your program, estimate P(D), where D = {a permutation of 1–12 is a derangement}.

c. From Section 2.3, we know the number of permutations of n items. (How many is that for n = 12?) Use this information and your answer to part (b) to estimate the number of derangements of the numbers 1 through 12.