# itertools module - combinations

Categories: python standard library

The `combination`

function returns a sequence of combinations of the values in the input iterable. A combination is every unique set of `r`

elements from the iterable. See this article for more information on combinations.

For example:

a = [1, 2, 3, 4] for i in itertools.combinations(a, r=2): print(i)

This returns:

(1, 2) (1, 3) (1, 4) (2, 3) (2, 4) (3, 4)

Notice that this list contains `(1, 2)`

but it doesn't contain `(2, 1)`

. Combinations do not take account of the order of the values, so `(1, 2)`

and `(2, 1)`

are considered to be the *same* combination.

This type of combination is often called combination *without replacement*. If we have four cards numbered 1 to 4, and we:

- Draw a card at random from the 4 cards.
- Draw a second card at random from the remaining 3 cards (ie without replacing the first card).

The set of possible combinations would be the ones listed above.

## combinations_with_replacement

`combinations_with_replacement`

is similar to `combinations`

except that input elements can be repeated. For example:

a = [1, 2, 3, 4] for i in itertools.combinations_with_replacement(a, r=2): print(i)

This adds some extra combinations: (1, 1), (2, 2), (3, 3), and (4, 4):

(1, 1) (1, 2) (1, 3) (1, 4) (2, 2) (2, 3) (2, 4) (3, 3) (3, 4) (4, 4)

The combination with replacement scanario is like this. We have four cards numbered 1 to 4, and we:

- Draw a card at random from the 4 cards.
- Make a note of the first card then put ot back in the deck.
- Draw a second card at random from the 4 cards.

This would make the extra combinations (1, 1), (2, 2) etc possible. Another example would be throwing a dice several times. Clearly the same number could appear more than once.

## See also

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