Permutation
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A permutation of a set of objects is any rearrangement (linear ordering) of the
objects. There are
(the factorial of
) permutations of a set with
objects.
An important question is how many ways to pick an -element subset of a set with
elements, where order matters. To find how many ways we can do this, note that for the first of the
elements, we have
different objects we can choose from. For the second element, there are
objects we can choose,
for the third, and so on. In general, the number of ways to permute
objects from a set of
is given by
.