Permutation vs. Combination: Know the Difference
By Shumaila Saeed || Updated on December 25, 2023
Permutation is an arrangement of items where order matters; combination is a selection where order does not.
Key Differences
Permutation refers to the arrangement of objects in a specific order, where the sequence is crucial. For example, the code '123' is different from '321'. Combination involves the selection of items without regard for order, where '123' is considered the same as '321'. Permutation focuses on sequences, while combination focuses on groups.
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Nov 19, 2023
When considering permutations, one must account for the different orders in which objects can appear. For instance, when arranging books on a shelf, the order in which they are arranged is a permutation. In contrast, combinations would look at the choice of books for the shelf, irrespective of order, caring only about which books are chosen, not the sequence.
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Nov 19, 2023
In mathematics, a permutation is often symbolized by 'nPr', denoting the number of ways to arrange 'n' objects taken 'r' at a time. Combination is denoted by 'nCr', representing the number of ways to choose 'r' objects from a set of 'n' without considering the order of selection.
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Nov 19, 2023
Permutations are typically used in scenarios where the arrangement is key, like in lottery numbers or passwords. Combinations are used when the concern is about presence or absence, like the combination of ingredients in a salad, regardless of the order they are added.
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Nov 19, 2023
To calculate permutations, one would use factorial operations considering all possible orders. For combinations, the formula divides the permutation by the factorial of the number of items chosen, effectively removing the sequence aspect.
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Nov 19, 2023
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Comparison Chart
Calculation
Factorial of the number of items (n!)
Factorial divided by the product of the factorials of the number of items and the difference between the number of items and the number chosen (n! / (r!(n-r)!))
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Use in Problems
Used when the problem is about arranging
Used when the problem is about selecting
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Permutation and Combination Definitions
Permutation
A permutation is a particular sequence of items.
The permutation of letters 'A,' 'B,' 'C' results in 'CBA' or 'BAC'.
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Combination
A combination is a selection of items without regard to the order.
The combination of fruits 'apple, banana, cherry' is the same as 'cherry, banana, apple'.
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Permutation
Permutation is the act of arranging all the members of a set into some sequence.
There are 6 permutations for the set {1, 2, 3}.
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Combination
Combination is the choice of items where sequence is irrelevant.
Selecting toppings for a pizza is an example of a combination.
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Permutation
Permutation is the action of changing the arrangement, or order, of items.
By permuting the digits of '321,' you get '213'.
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Combination
In mathematics, combination is the number of ways to choose items from a group, without regard to the order.
From five flavors, there are ten combinations to choose three.
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Permutation
The process of altering the order of a given set of objects in a group.
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Nov 07, 2023
Permutation
The result of such a process; a rearrangement or recombination of elements
Permutations of gene order.
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Combination
An alliance of persons or parties for a common purpose; an association.
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Permutation
A complete change; a transformation
The country's permutation into a modern democracy.
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Combination
A sequence of numbers or letters used to open a combination lock.
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Permutation
One of the ways something exists, or the ways a set of objects can be ordered.
Which permutation for completing our agenda items makes the most sense?
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Combination
(Mathematics) One or more elements selected from a set without regard to the order of selection.
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Permutation
(mathematics) A one-to-one mapping from a finite set to itself.
This permutation takes each element to the one following it, with the last mapped back to the first.
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Combination
The act of combining, the state of being combined or the result of combining.
These guidelines should be followed in combination with those given last week.
She took a dangerous combination of alcohol and heroin.
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Permutation
An ordering of a finite set of distinct elements.
There are six permutations of three elements, e.g. {abc, acb, bac, bca, cab, cba}.
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Permutation
(music) A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde.
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Combination
A sequence of numbers or letters used to open a combination lock.
The combination to their safe was the date of birth of their first child.
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Permutation
The act of permuting; exchange of the thing for another; mutual transference; interchange.
The violent convulsions and permutations that have been made in property.
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Combination
(mathematics) One or more elements selected from a set without regard to the order of selection.
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Permutation
An event in which one thing is substituted for another;
The replacement of lost blood by a transfusion of donor blood
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Combination
(billiards) A combination shot; a billiard; a shot where the cue ball hits a ball that strikes another ball on the table.
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Permutation
The act of changing the arrangement of a given number of elements
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Permutation
Complete change in character or condition;
The permutations...taking place in the physical world
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Combination
A rapid sequence of punches or strikes in boxing or other combat sports.
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Combination
The act or process of combining or uniting persons and things.
Making new compounds by new combinations.
A solemn combination shall be madeOf our dear souls.
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Permutation
In mathematics, permutation is the number of ways to order a subset.
There are 24 permutations of four different books.
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Combination
The result of combining or uniting; union of persons or things; esp. a union or alliance of persons or states to effect some purpose; - usually in a bad sense.
A combination of the most powerful men in Rome who had conspired my ruin.
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Permutation
Permutation refers to a rearrangement of elements.
The permutation of the word 'LOG' can also form 'GOL'.
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Combination
The act or process of uniting by chemical affinity, by which substances unite with each other in definite proportions by weight to form distinct compounds.
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Combination
The different arrangements of a number of objects, as letters, into groups.
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Combination
A collection of things that have been combined; an assemblage of separate parts or qualities
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Combination
A sequence of numbers or letters that opens a combination lock;
He forgot the combination to the safe
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Combination
A group of people (often temporary) having a common purpose;
They were a winning combination
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Combination
An alliance of people or corporations or countries for a special purpose (formerly to achieve some antisocial end but now for general political or economic purposes)
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Combination
The act of arranging elements into specified groups without regard to order
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Combination
Combination is the process of combining items into a single set.
A salad is a combination of various vegetables.
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Combination
Combination refers to a grouping of elements where order does not matter.
The combination of '2, 3, 5' is the same as '5, 2, 3'.
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Repeatedly Asked Queries
What is a simple definition of permutation?
Permutation is the arrangement of objects in a specific order.
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Nov 19, 2023
Can you give a real-world example of a permutation?
A lock combination is a real-world example of a permutation because the order of numbers matters.
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Are permutations always greater than or equal to combinations?
Yes, because permutations consider order, there are always as many or more permutations than combinations.
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Nov 19, 2023
How is permutation calculated?
Permutation is calculated using the factorial of the number of items arranged at a time.
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Nov 19, 2023
How do you denote a permutation mathematically?
Mathematically, a permutation is denoted as nPr.
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Nov 19, 2023
How do you denote a combination mathematically?
Mathematically, a combination is denoted as nCr.
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Nov 19, 2023
What is a real-world example of a combination?
A hand in poker is a combination since the order of cards does not affect the hand.
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How do combinations differ from permutations?
Combinations involve selecting items without concern for the order they are in.
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Nov 19, 2023
Does changing the order of a combination change it?
No, the order of items in a combination does not change the combination.
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Is repetition allowed in permutations?
Yes, permutations can allow for repetition, depending on the context.
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Nov 19, 2023
What are applications of combinations?
Combinations are used in situations like choosing lottery numbers where order does not matter.
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Nov 19, 2023
How is combination calculated?
Combination is calculated using the formula nCr, which accounts for the selection of r items from n without order.
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Nov 19, 2023
How do permutations apply to passwords?
Each possible arrangement of characters in a password is a permutation.
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Do all permutations have a corresponding combination?
Yes, for any set of items, there is a corresponding combination for each permutation set.
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Nov 19, 2023
Are permutations used in statistics?
Yes, permutations are used in statistics to calculate probabilities where order is important.
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Nov 19, 2023
How does permutation affect the total number of outcomes?
Permutation increases the total number of outcomes due to the significance of order.
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Nov 19, 2023
Can you switch between permutation and combination?
You can switch calculations depending on whether order is relevant (permutation) or not (combination).
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Nov 19, 2023
Does combination affect the total number of possible outcomes?
Combination affects the total number of outcomes by considering the selection without regard to order.
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Nov 19, 2023
Can combinations have repeated items?
No, combinations do not consider repetition since the order does not matter.
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Nov 19, 2023
Are combinations used in statistics?
Yes, combinations are used in statistical calculations where the selection is important but order is not.
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Nov 19, 2023
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About Author
Written by
Shumaila SaeedShumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.
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