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
.