combinations and permutations

Learn combinatorics with combinations and permutations.

combinations and permutations

combinations(iterable, r) produces the combinations (unordered) of length r from a set. permutations(iterable, r) produces the permutations (ordered). Both are in the itertools module.

Example: list(combinations([1, 2, 3], 2)) returns [(1, 2), (1, 3), (2, 3)]. list(permutations([1, 2, 3], 2)) returns [(1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2)]. Use permutations if order matters, combinations otherwise.

When to use?

If you need an unordered selection from a list, use combinations. Example: choosing 2 people from a team. For ordered selection, use permutations. Example: choosing a president and a deputy.

Both return an iterator; you can see the results with list(). If r is not given, permutations tries all lengths; combinations requires r. Computational complexity grows quickly; use carefully on large data.

Exercise Choose pairs with combinations

Start with from itertools import combinations. Generate all pair combinations with result = list(combinations([1, 2, 3], 2)). Then print with print(result).

Show example solution

# Generate pair combinations
from itertools import combinations

result = list(combinations([1, 2, 3], 2))
print(result)

Test yourself

Match combinations and permutations

combinations

Unordered
permutations

Ordered
(1, 2)

Combination example
(2, 1)

Permutation example
Which one for choosing president and deputy?
- combinations
- islice
- chain
- permutations
Show answer

permutations — Permutations. Since order matters, permutations is used.

combinations import line

from itertools import ____

result = list(combinations([1, 2, 3], 2))
print(result)

Show answer

from itertools import combinations

result = list(combinations([1, 2, 3], 2))
print(result)

Next lesson: groupby

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