  In this paper we study the number of key exchanges required by Hoare's FIND
algorithm (also called Quickselect) when operating on a uniformly distributed
random permutation and selecting an independent uniformly distributed rank.
After normalization we give a limit theorem where the limit law is a perpetuity
characterized by a recursive distributional equation. To make the limit theorem
usable for statistical methods and statistical experiments we provide an
explicit rate of convergence in the Kolmogorov--Smirnov metric, a numerical
table of the limit law's distribution function and an algorithm for exact
simulation from the limit distribution. We also investigate the limit law's
density. This case study provides a program applicable to other cost measures,
alternative models for the rank selected and more balanced choices of the pivot
element such as median-of-$2t+1$ versions of Quickselect as well as further
variations of the algorithm.
