Question

What is a permutation?

Answer 1

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

Explanation:

For example if our collect were
`color(white)("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 `1st` item; then only `3` remaining choices for the `2nd` item.
So the number of permutations of `2` fruits selected from a collection of `4` fruits would be `4xx3 = 12`