EF Definition

Section 21.2 Definition

We often want to count how many ways we can “mix up” the objects in a collection.

Once you have written the elements of a finite set in some order, think of a permutation as a way of re-ordering them.

Figure 21.2.3 contains tables of values for all six possible permutations of the set

A = {a, b, c} .

We have grouped them according to: all elements fixed; one element fixed and two mixed; all elements mixed.

$x$	$a$	$b$	$c$
${id}_{A} (x)$	$a$	$b$	$c$

Figure 21.2.3. All possible permutations on three objects.

Elementary Foundations: An introduction to topics in discrete mathematics