WordGarden.iopermutation
C2Pronunciation
UK
- /pˌɜːmjuːtˈeɪʃən/
US
- /ˌpɜrmjuˈteɪʃən/
Meanings
Noun
one of the possible arrangements or reordered versions of a set of things
an ordered arrangement of elements considered in combinatorics or related mathematics
Beyond the definition
Imagine you have three blocks: red, blue, and green. A permutation is any way you can put those same blocks in order. Red-Blue-Green is one, and Blue-Red-Green is another. The main idea is simple: the items stay the same, but their order changes.
This idea is especially important in math and computer science when people count possibilities or build different sequences. Think about passwords: each different order of the same letters, numbers, or symbols creates a different result. You might also talk about different orders of cards, steps, or choices when the exact order matters.
A permutation refers to an arrangement of objects in a specific order. It's not just which items are present, but the sequence in which they appear that matters. Think of it like this: if you have a team of five runners, the order they finish a race creates a different permutation each time – even if the same five runners are always involved!
The concept originates from mathematics, specifically combinatorics, where it's used to calculate the number of possible arrangements of items. For example, how many ways can you arrange the letters in the word "CAT"? There are six permutations: CAT, CTA, ACT, ATC, TAC, and TCA.
However, "permutation" isn't limited to math class. It also appears in broader discussions about different possible arrangements or outcomes. A political strategist might talk about "permutations of voting patterns," meaning different possible results based on how people vote. A choreographer might explore "permutations of dance steps," trying out various sequences to create a unique routine.
In computer science, permutations are crucial for algorithms involving sorting, searching, and cryptography. They help determine the number of possibilities and ensure digital security. So, whether you're calculating probabilities, planning a schedule, or simply rearranging furniture, understanding permutation means recognizing that order matters – and exploring all the different ways things can be arranged.
Examples
- 1
Password security
The password program checks every possible permutation of the six numbers.
- 2
Math
There are 120 different permutations of five different letters.
- 3
Seating plan
The seating chart changed again, but it was still a permutation of the same eight names.
- 4
Design testing
The team tested several permutations of the page layout before choosing the final design.
More examplesFewer examples
- 5
Schedule planning
By Friday, we had tried every permutation and combination of the schedule.
- Phraseevery permutation and combination
every possible way of arranging or changing something
See also
Forms and spellings
2 forms open this card.
Main spelling
- permutationnoun
Forms
- permutationspluralnoun