What is a permutation?

Nov 13, 2015

A permutation is a sequenced selection of items from some collection.

Explanation:

For example if our collect were
$\textcolor{w h i t e}{\text{XXX"){"an apple", "a banana", "an orange", "a melon}}$

One permutation would be
color(white)("XXX")<"a melon","a banana","an apple","an orange">
note that this is a different permutation than
color(white)("XXX")<"a banana", "a melon", "an apple", "an orange">
(the order is significant).

Often a permutation may be specified as only a certain number of items selected from the given base collection.

For example, one possible permutation of $2$ fruit from the collection above would be
color(white)("XXX")<"a banana", "an apple">

Sometimes we are interested in how many different permutations are possible.

Again using the collection of fruit as an example,
there are $4$ possible fruit which could be picked as the $1 s t$ item; then only $3$ remaining choices for the $2 n d$ item.
So the number of permutations of $2$ fruits selected from a collection of $4$ fruits would be $4 \times 3 = 12$