How do you calculate combinations in python?

Do you want iteration? itertools.combinations. Common usage:

>>> import itertools
>>> itertools.combinations('abcd',2)

>>> list(itertools.combinations('abcd',2))
[('a', 'b'), ('a', 'c'), ('a', 'd'), ('b', 'c'), ('b', 'd'), ('c', 'd')]
>>> [''.join(x) for x in itertools.combinations('abcd',2)]
['ab', 'ac', 'ad', 'bc', 'bd', 'cd']

If you just need to compute the formula, math.factorial can be used, but is not fast for large combinations, but see math.comb below for an optimized calculation available in Python 3.8+:

import math

def nCr(n,r):
    f = math.factorial
    return f(n) // f(r) // f(n-r)

if __name__ == '__main__':
    print nCr(4,2)

Output:

6

As of Python 3.8, math.comb can be used and is much faster:

>>> import math
>>> math.comb(4,2)
6

❮ Math Methods

Example

Find the total number of possibilities to choose k things from n items:

# Import math Library
import math

# Initialize the number of items to choose from
n = 7

# Initialize the number of possibilities to choose
k = 5

# Print total number of possible combinations
print (math.comb(n, k))

The result will be:

21

Run Example »

Definition and Usage

The math.comb() method returns the number of ways picking k unordered outcomes from n possibilities, without repetition, also known as combinations.

Note: The parameters passed in this method must be positive integers.

Syntax

Parameter Values

Note: If the value of k is greater than the value of n it will return 0 as a result.

Note: If the parameters are negative, a ValueError occurs. If the parameters are not integers, a TypeError occurs.

Technical Details

❮ Math Methods

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

from itertools import permutations 

perm = permutations([1, 2, 3]) 

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

from itertools import permutations 

perm = permutations([1, 2, 3], 2) 

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

from itertools import combinations

comb = combinations([1, 2, 3], 2)

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

from itertools import combinations 

comb = combinations([1, 2, 3], 2) 

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

from itertools import combinations 

comb = combinations([2, 1, 3], 2) 

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

from itertools import combinations_with_replacement 

comb = combinations_with_replacement([1, 2, 3], 2) 

for i in list(comb): 

    print (i) 

Output:

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

How do you find the number of combinations in Python?

How does combinations work in Python?

How do you calculate number of combinations?