 # 5 Difference Between Permutation and Combination

Permutation and combination are two very important terms in mathematics and statistics. Both permutation and combination are used in mathematics and probability. These terms are used in our daily life as our passwords for example our passwords are the combination of the numbers in a specific order. Many of us get confused when we see the terms permutation and combination. In many cases, we think that permutation and combination are the same but these are different from each other. In this article, we will discuss the difference between permutation and combination in detail, and their examples for better understanding.

## Permutation Vs Combination

 Sr.no Permutation Combination 1 The meaning of permutation is an arrangement of a given number of data in all possible ways The meaning of combination is a selection of a group of numbers or letters from the total objects or numbers. 2 In permutation order of numbers and objects are matters like ab is different from ba. On the other hand in combination order of objects does not matter eg. ba is equal to ab. 3 A permutation is a way to arrange things, colors, peoples, digits, numbers, and alphabets. While the combination is a way of selecting a menu item, clothes, subjects, food, etc. 4 From a single combination, a number of permutations are extracted. While from a single permutation only one combination is derived. 5 A permutation is how many arrangements are extracted from a set of objects. On the other hand, the combination is a selection of groups from the set of objects.

## Permutation

it is a way of expressing numbers and letters in which, the order of numbers or letters matters. The simple means of permutation is to arrange a given number or data in any way as per order. Suppose we have three letters a,b, and c and we have to choose 2 out of them. In that case we have possible arrangements are ab,bc,ca,ba,CB,ac.

We have a total of six arrangements. In this, the order of the letters is very important for example ca and ac is different from each other.

Same way if we have to 3 letters from ABC we have possible arrangements are ABC,bac,CBA,ACB,BCA,cab. We have total arrangements are 6.

Mathematical formula of permutation

nPr which means n!/(n-r)!

In first case we have n=3 and r= 2

So nPr = 3!/(3-2)! =3x2x1/1 = 6

Another solution nPn = n!

And nP0 = 1

### Types of permutation

There are two types of permutation

Permutation with repetition.

Permutation without repetition.

#### Permutation with repetition

In this case of permutation, repeat words or letters are used again and again like 3333,2211,5542, etc. In that case number of permutation increase. For example, we have 1,2,3,4 and we have to choose 4 numbers. we want to include 1123, 1111 like this. This is a case of repetition permutation. In that case, we have the choice to choose one number again and again so we have four options to choose every letter of permutation. So we have a total number of permutations are 4x4x4x4= 256.

#### Permutation without repetition

This is the general case of permutation in which the number of choices is decreased with the arrangement of the first letter or data. Eg: we have number 1,2,3,4 and we have to choose all of them without repetition. In this case, we have 4 choices choose the first number of arrangements. When we choose the first number we have only 3 choices to choose the second number and these processes stay continued up to the last number. So we have total arrangements are 4! = 4x3x2x1 = 24.

## Combination

The simple meaning of combination is a selection of a group of numbers or letters from the total objects or numbers. In this order, the numbers or letters don’t matter. If we have three letters a,b, and c and we have to choose 2 out of them the total possible selection we have ab, bc, and ac. In this case, we don’t choose ba, bc, and ca because in combination these are the same.

ab=ba

bc=cb

ac=ca

In the above example, we have only 3 combinations.

Mathematical formula

nCr = n!/r!x(n-r)!

Eg: If we have three letters a,b,c and we have to choose 2 out of them the total possible selection.

n=3, r=2

3C2 = 3!/2!x(3-2)!

= 3!/2!

= 6/2 = 3

## Example of permutation and combination.

Suppose we have 5 letters a,b,c,d,e and we have to choose and we have to select only 3 out of 5. In this example if we talk about the permutation without repetition we have a total permutation are 5P3 which is equal to = 5!/(5-3)! = 5x4x3x2!/2! = 60. And with repetition permutation we have total permutation = 5x5x5 = 125.

For the combination in the obove example we have total combination are 5C3 = 5!/3!x(5-3)! = 5x4x3!/3!x2x1 = 10.

By this example, all your doubts will be clear. ## The main difference between permutation and combination

1. The meaning of permutation is an arrangement of given numbers or data in all possible ways. The meaning of combination is the selection of a group of numbers or letters from the total objects or numbers.
2. In permutation order of numbers and objects are matters like ab is different from ba. On the other hand in combination order of objects does not matter eg ba is equal to ab.
3. The permutation is a way to arrange things, colors, peoples, digits, numbers, and alphabets. While the combination is a way of selecting a menu item, clothes, subjects, food, etc.
4. From a single combination, a number of permutations are extracted. While from a single permutation only one combination is derived.
5. The permutation is how many arrangements are extracted from a set of objects. On the other hand, a combination is a selection of groups from a set of objects.

## Conclusion

Both the terms permutation and the combination are very important in mathematics. We learn both these terms before the probability because permutation and combination play an important role in probability. we use them for our bank account security. Buy the above article it is clear that both permutation and combination are different from each other. The very important about permutation and combination is permutation is always higher than the combination results.

This is about the difference between permutation and the combination. We hope you understand the topic very well. For more interesting differences please visit our website.

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