# Permutation and Combination in Python

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 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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