Difference Between Permutation and
Combination
Last updated on August 26, 2017 by Surbhi S
In mathematics,
you might have heard the notions of permutation and combination end number of times, but have
you ever imagined that these two are different concepts? The fundamental difference between
permutation and combination is the order of objects, in permutation the order of objects is very
important, i.e. the arrangement must be in the stipulated order of the number of objects, taken
only some or all at a time.
As against this, in the case of a combination, the order does not matter at all. Not only in
mathematics but in practical life too, we go through with these two concepts regularly. Although,
we never notice it. So, take a read of the article carefully, to know how these two concepts are
different.
Content: Permutation Vs Combination
1. Comparison Chart
2. Definition
3. Key Differences
4. Example
5. Conclusion
Comparison Chart
Basis for
Permutation Combination
Comparison
Permutation refers to the different Combination refers to several ways of
Meaning ways of arranging a set of objects choosing items from a large set of objects,
in a sequential order. such that their order does not matters.
Order Relevant Irrelevant
Denotes Arrangement Selection
What is it? Ordered elements Unordered sets
How many different arrangement
How many different groups can be chosen
Answers can be created from a given set of
from a larger group of objects?
objects?
Multiple permutation from a single Single combination from a single
Derivation
combination. permutation.
Definition of Permutation
We define permutation as different ways of arranging some or all the members of a set in a
specific order. It implies all the possible arrangement or rearrangement of the given set, into
distinguishable order.
For example, All possible permutation created with letters x, y, z –
By taking all three at a time are xyz, xzy, yxz, yzx, zxy, zyx.
By taking two at a time are xy, xz, yx, yz, zx, zy.
Total number of possible permutations of n things, taken r at a time, can be calculated as:
Definition of Combination
The combination is defined as the different ways, of selecting a group, by taking some or all the
members of a set, without the following order.
For example, All possible combinations chosen with letter m, n, o –
When three out of three letters are to be selected, then the only combination is mno
When two out of three letters are to be selected, then the possible combinations are mn,
no, om.
Total number of possible combinations of n things, taken r at a time can be calculated as:
Key Differences Between Permutation and Combination
The differences between permutation and combination are drawn clearly on the following
grounds:
1. The term permutation refers to several ways of arranging a set of objects in a sequential
order. Combination implies several ways of choosing items from a large pool of objects,
such that their order is irrelevant.
2. The primary distinguishing point between these two mathematical concepts is order,
placement, and position, i.e. in permutation characteristics mentioned above does matter,
which does not matter in the case of the combination.
3. Permutation denotes several ways to arrange things, people, digits, alphabets, colours,
etc. On the other hand, combination indicates different ways of selecting menu items,
food, clothes, subjects, etc.
4. The permutation is nothing but an ordered combination while Combination implies
unordered sets or pairing of values within specific criteria.
5. Many permutations can be derived from a single combination. Conversely, only a single
combination can be obtained from a single permutation.
6. Permutation answers How many different arrangements can be created from a given set
of objects? As opposed to the combination which explains How many different groups
can be picked from a larger group of objects?
Example
Suppose, there is a situation where you have to find out the total number of possible samples of
two out of three objects A, B, C. In this question, first of all, you need to understand, whether the
question is related to permutation or combination and the only way to find this out is to check
whether the order is important or not.
If the order is significant, then the question is related to permutation, and possible samples will
be, AB, BA, BC, CB, AC, CA. Where, AB is different from BA, BC is different from CB and
AC is different CA.
If the order is irrelevant, then the question is related to the combination, and the possible samples
will be AB, BC and CA.
Conclusion
With the above discussion, it is clear that permutation and combination are different terms,
which are used in mathematics, statistics, research and our day to day life. A point to remember,
regarding these two concepts is that, for a given set of objects, permutation will always be higher
than its combination.
