  We discuss efficient methods for unranking derangements and m\'enage
permutations. That is, we will provide an algorithm to efficiently extract the
$k$-th earliest such permutation under the lexicographic ordering. We will show
that this problem can be reduced to the problem of computing the number of
restricted permutations with a given prefix, and then we will use rook theory
to solve this counting problem. This has applications to combinatorics,
probability, statistics, and modeling.
