Derangements, a favorite topic in combinatorics,
are usually studied using the inclusion-exclusion 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 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.