# Generating Permutations

In today's post we're going to discuss the generation of permutations.

Often, in combinatorics problems, we are interested in *how many* different
instances or configurations of a particular thing we can have (what we'll call
"enumeration" or "counting"). However, that is different from wanting to
actually see all of those configurations. Indeed, if we are counting
something with an astronomical number of configurations, we don't want
to try to list all of them.

However, as usual, Donald Knuth, who covers the topic of permutation
generation in Volume 4A of his classic work,
__The Art of Computer Programming__,
uncovers …