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Difference Between Permutation and Combination (With Table)

Permutation vs Combination

A permutation is for lists where does order matters but in Combination, it doesn’t. Practically, both involve selecting a subset from several elements.

With a simple example, when you return from the market, if your mom asks about the price, you should say it 235 (which is actual), not 325 or 532. That’s Permutation.  When mom asks what vegetables did you bring then you say the whole list of vegetables randomly (potato, onion,   brinjal, tomato, etc). That’s called Combination.


 

Comparison Table Between Permutation and Combination (in Tabular Form)

Parameter of comparisonPermutationCombination
Definition‘Permutation’ is a collection of an object where the order of objects is important.‘Combination’ is a collection of objects where an order isn’t important.
RepresentsArrangementSelection
Order effectsYesNo
DerivedMultiple Permutation  derived from a single combinationOnly single Combination may be derived from a Permutation
DenotedThe number of arrangements is denoted byThe number of arrangements is denoted by

 

What is Permutation?

‘Permutation’ is defined as an arrangement that can be done using some of the objects or items in an ordered manner. It’s all about arrangement and denoted by.

Suppose, a smartphone is locked by a PIN code which is 9396. To unlock, it won’t open if you enter 9693, because there is a different ordering for your smartphone’s PIN. It’s an arrangement that depends on the order. So, the order is important to unlock or get the correct PIN.

 

What is Combination?

‘Combination’ is defined as the selection that can be done using some of the items where order does not matter. ‘Combination’ is represented by.


Main Differences Between Permutation and Combination

The difference Between Permutation and Combination are clearly explained below:

  • Placement and order is the main difference between permutation and combination. In permutation, we are restricted to comply with an order but in combination, there is no such restriction.
  •  A permutation is just an arrangement of the things where the arrangement will be in a specific order. The combination is a selection where the selection is without any specific order.
  • In Permutation, the number of arrangements is denoted by nPr. The combination is represented by
  • Multiple permutations can be derived from a single combination but only a single combination may be derived from one permutation.
  • A permutation is the choice of ‘r’ things from the group or set of ‘n’ things with the order. The combination is a selection of ‘r’ things from the large set or group of ‘n’ things without any specific order.

 

Conclusion

After knowing the above differences thoroughly, it was understood that Permutation and Combination are completely different terms which are the so-called ways with the field of Mathematics. In these two different terms, we are always concerned about arrangement and selection. It’s necessary to know that for a set of objects, Permutation is always much more than it’s Combination.


 

Word Cloud for Difference Between Permutation and Combination

The following is a collection of the most used terms in this article on Permutation and Combination. This should help in recalling related terms as used in this article at a later stage for you.

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