What is a permutation?

1 Answer
Alan P.
Nov 13, 2015

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#

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