Derangements, a favorite topic in combinatorics, are usually studied using the inclusionexclusion principle, to calculate the number of derangements of n objects, as well as the
probability of a derangement occurring. This paper briefly presents this solution, as well
as a second fairly standard solution using a bijection and recursion method, and then
proceeds to solve for the probability of a derangement using the binomial inversion
formula, which is derived in the final section of the paper. To show the utility and
elegance of this approach, the expected value of correct assignments is also calculated if
n objects are arranged at random.