# Permutation and Combination in Python

• Difficulty Level : Easy
• Last Updated : 19 Jul, 2022

Python provides direct methods to find permutations and combinations of a sequence. These methods are present in itertools package.

## Permutation

First import itertools package to implement the permutations method in python. This method takes a list as an input and returns an object list of tuples that contain all permutations in a list form.

## Python3

 `# A Python program to print all  ` `# permutations using library function  ` `from` `itertools ``import` `permutations  ` ` `  ` `  `# Get all permutations of [1, 2, 3]  ` `perm ``=` `permutations([``1``, ``2``, ``3``])  ` ` `  `# Print the obtained permutations  ` `for` `i ``in` `list``(perm):  ` `    ``print` `(i)  `

Output:

```(1, 2, 3)
(1, 3, 2)
(2, 1, 3)
(2, 3, 1)
(3, 1, 2)
(3, 2, 1)```

It generates n! permutations if the length of the input sequence is n.
If want  to get permutations of length L then implement it in this way.

## Python3

 `# A Python program to print all  ` `# permutations of given length  ` `from` `itertools ``import` `permutations  ` ` `  `# Get all permutations of length 2  ` `# and length 2  ` `perm ``=` `permutations([``1``, ``2``, ``3``], ``2``)  ` ` `  `# Print the obtained permutations  ` `for` `i ``in` `list``(perm):  ` `    ``print` `(i)  `

Output:

```(1, 2)
(1, 3)
(2, 1)
(2, 3)
(3, 1)
(3, 2)```

It generates nCr * r! permutations if the length of the input sequence is n and the input parameter is r.

## Combination

This method takes a list and an input r as an input and return an object list of tuples which contain all possible combination of length r in a list form.

## Python3

 `# A Python program to print all  ` `# combinations of given length ` `from` `itertools ``import` `combinations ` ` `  `# Get all combinations of [1, 2, 3] ` `# and length 2 ` `comb ``=` `combinations([``1``, ``2``, ``3``], ``2``) ` ` `  `# Print the obtained combinations ` `for` `i ``in` `list``(comb): ` `    ``print` `(i) `

Output:

```(1, 2)
(1, 3)
(2, 3)```

1. Combinations are emitted in lexicographic sort order of input. So, if the input list is sorted, the combination tuples will be produced in sorted order.

## Python3

 `# A Python program to print all  ` `# combinations of a given length  ` `from` `itertools ``import` `combinations  ` ` `  `# Get all combinations of [1, 2, 3]  ` `# and length 2  ` `comb ``=` `combinations([``1``, ``2``, ``3``], ``2``)  ` ` `  `# Print the obtained combinations  ` `for` `i ``in` `list``(comb):  ` `    ``print` `(i) `

Output:

```(1, 2)
(1, 3)
(2, 3)```

2. Elements are treated as unique based on their position, not on their value. So if the input elements are unique, there will be no repeat values in each combination.

## Python3

 `# A Python program to print all combinations  ` `# of given length with unsorted input.  ` `from` `itertools ``import` `combinations  ` ` `  `# Get all combinations of [2, 1, 3]  ` `# and length 2  ` `comb ``=` `combinations([``2``, ``1``, ``3``], ``2``)  ` ` `  `# Print the obtained combinations  ` `for` `i ``in` `list``(comb):  ` `    ``print` `(i) `

Output:

```(2, 1)
(2, 3)
(1, 3)```

3. If we want to make a combination of the same element to the same element then we use combinations_with_replacement.

## Python3

 `# A Python program to print all combinations  ` `# with an element-to-itself combination is  ` `# also included  ` `from` `itertools ``import` `combinations_with_replacement  ` ` `  `# Get all combinations of [1, 2, 3] and length 2  ` `comb ``=` `combinations_with_replacement([``1``, ``2``, ``3``], ``2``)  ` ` `  `# Print the obtained combinations  ` `for` `i ``in` `list``(comb):  ` `    ``print` `(i)  `

Output:

```(1, 1)
(1, 2)
(1, 3)
(2, 2)
(2, 3)
(3, 3) ```

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