Permutation vs Combinations – In this article, you will be able to learn the meaning, differences, and formulas as well as the examples between the words combination and permutation.
In addition, permutation is a way to use math to figure out how many ways there are to arrange a set of things, while combination is a mathematical method for figuring out how many different ways a group of things can be put together.
In fact, in the field of mathematics, permutations and combinations are groups or arrangements of things, like people, numbers, and objects. Besides, the main difference between permutations and combinations is that order matters in permutations but not in combinations.
Furthermore, the examples of permutations are things like putting people, digits, numbers, alphabets, letters, and colors in different ways. Some examples of combinations are the choice of menu, food, clothes, subjects, and team.
Table of contents
What is the meaning of Permutations?
A permutation is a way to use math to figure out how many ways there are to arrange a set of things when the order of the arrangements matters. In many math problems, you have to choose only a few things from a set and put them in a certain order.
Additionally, people often mix up permutations with another math technique called “combinations.”
What is the meaning of Combinations?
A combination is a mathematical method for figuring out how many different ways a group of things can be put together when the order doesn’t matter.
Additionally, you can choose the items for a combination in any order.
Formula for Combinations and Permutations
What is the Formula for Combination?
The combination formula is:
 | = | number of combinations |
 | = | total number of objects in the set |
 | = | number of choosing objects from the set |
What is Formula for Permutation?
The formula for permutation is P(n, r) = n!/(n-r)!” many ways can you arrange “r” from a set of “n” if the order matters?” It is a general form of the formula. Also, you can calculate a permutation by hand by writing down all the possible permutations.
The Difference Between Permutations and Combinations
The difference between a combination and a permutation is how they are arranged. The table below shows the difference between the two.
| Permutation | Combination |
| Permutation is the different ways that a set of things can be put in order. | Combination is the different ways to choose things from a large group of things where the order doesn’t matter. |
| You care about the order. | It doesn’t matter how you put things together. |
| It is used for things of different kind. | It is used for things of similar kind. |
| It is used to utilized whenever there is a requirement for order or sequence in the arrangement. | It is used to find out how many different groups can be made. |
| It is orderings | It is a choices |
Permutations vs Combinations Examples and Uses
Example and Uses of Permutation
Example 1:
Find the different three-digit codes which can be formed using the digits 1, 2, 4, 5, 8, and 9, also, by using the concepts of the difference between permutations and combinations.
Solution:
The given digits are 1, 2, 4, 5, 8, 9.We need to form a three-digit code from the five digits given. In addition to that, using the concepts from the difference between permutations and combinations, here we need to find the arrangements and hence we use the formula of permutations.
Answer:
Therefore we can form 60 three-digit codes from the given 5 digits.
This example and uses of Permutation is from cuemath.com
Example and Uses of Combination
Example 2:
In how many ways can a coach form a team of 2 players from among the six players in the academy? Try to use the concepts from the difference between permutations and combinations to find the possible solution.
Solution:
Here the aim is to select 2 players from the available 6 players. This is a case of forming a group, and hence we use the formula of combinations to find the possible number of teams that can be formed.
Here we have n = 6 and r = 2
Answer: Hence the coach can form 15 different teams of 2 players from the 6 players.
This example and uses of Combination is from cuemath.com
A permutation is putting things or numbers in a different order while combinations are a way to choose objects or numbers from a group or collection in a way that doesn’t matter what order the objects are in.
The formula for a permutation is: P(n,r) = n! / (n-r)!
The formula for a combination is : n C r = n ! ( n − r ) ! r !
The difference between a combination and a permutation is how they are arranged. With permutations, we care about the order of the elements, but not with combinations.
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Summary
In summary, we have discussed “Permutation vs Combination (Differences, Formulas, and Meaning)”. Both permutation and combination are used in every branch of mathematics. As a result, it is a combination if the order doesn’t matter. If the order matters, this is called a permutation, and we also discussed the permutation vs combination examples.
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