Difference Between Permutation and Combination

The difference between permutation and combination is that for permutation the order of the members is taken into consideration but for combination orders of members does not matter. For example, the arrangement of objects or alphabets is an example of permutation but the selection of a group of objects or alphabets is an example of combination. Learn in detail here: Permutation And Combination.

Definition of Permutation and Combination

Permutation: Permutation can simply be defined as the several ways of arranging few or all members within a specific order. It is the process of legibly arranging from chaos. This is what is termed as a Permutation.

Combination: The combination is a process of selecting the objects or items from a set or the collection of objects, such that (unlike permutations) the order of selection of objects does not matter. It refers to the combination of N things taken from a group of K at a time without repetition.

What is the Difference between Permutation and Combination?

Combination, on the other hand, can simply be defined as the method of selecting a group by taking up some or all members of a set. There is no particular order that is used to follow while combining elements of a set.

There are a lot of different ways of making up a combination and they are all right in their own ways; as there is no particular method of figuring out a combination the “right” way. Thus, this is defined as a combination. Using the combination formula, one can easily get the combination for any set.

Difference between Permutation and Combination
Permutation Combination
The different ways of arranging a set of objects into a sequential order are termed as Permutation. One of the several ways of choosing items from a large set of objects, without considering an order is termed as Combination.
The order is very relevant. The order is quite irrelevant.
It denotes the arrangement of objects. It does not denote the arrangement of objects.
Multiple permutations can be derived from a single combination. From a single permutation, only a single combination can be derived.
They can simply be defined as ordered elements. They can simply be defined as unordered sets.

Thus, these are the key differences between Permutation and Combination. It is important to understand how they differ from one another.

Example

Suppose, we have to find the total number of probable samples of two out of three objects X, Y, Z. Here, first of all, you have to understand whether the problem is relevant to permutation or combination. The only means to find it is to check whether the order is necessary or not.

If the order is important, then the problem is related to permutation, and the possible number of samples will be, XY, YX, YZ, ZY, XZ, ZX. In this case, XY is distinct from the sample YX, YZ is distinct from the sample ZY and XZ is distinct from the sample ZX.

If the order is unnecessary, then the question is relevant to the combination, and the possible samples will be XY, YZ and ZX.

Frequently Asked Questions on Difference Between Permutation and Combination

What are permutation and combination?

A permutation is a method of arranging all the members in order. The combination is selection of elements from a collection.

What is the example of permutation and combination?

Suppose A and B are two elements then they can be arranged in two ways only AB or BA, this is called a permutation.
Now if we there is one way to select A and B, then we select both of them.

What is the formula for permutation?

The formula for permutation is given by:
nPr = (n!)/(n-r)!
where n is the number of different elements
r is the arrangement pattern of the element
Both r and n are positive integers

What is the formula for a combination?

The formula for combination is given by:
nCr = (n!) /[r! (n-r)!]

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