# python – Generating permutations with repetitions

## python – Generating permutations with repetitions

You are looking for the Cartesian Product.

In mathematics, a Cartesian product (or product set) is the direct product of two sets.

In your case, this would be `{1, 2, 3, 4, 5, 6}` x `{1, 2, 3, 4, 5, 6}`.
`itertools` can help you there:

``````import itertools
x = [1, 2, 3, 4, 5, 6]
[p for p in itertools.product(x, repeat=2)]
[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3),
(2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3),
(5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)]
``````

To get a random dice roll (in a totally inefficient way):

``````import random
random.choice([p for p in itertools.product(x, repeat=2)])
(6, 3)
``````

Youre not looking for permutations – you want the Cartesian Product. For this use product from itertools:

``````from itertools import product
for roll in product([1, 2, 3, 4, 5, 6], repeat = 2):
print(roll)
``````

#### python – Generating permutations with repetitions

In python 2.7 and 3.1 there is a `itertools.combinations_with_replacement` function:

``````>>> list(itertools.combinations_with_replacement([1, 2, 3, 4, 5, 6], 2))
[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 3), (2, 4),
(2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6),
(5, 5), (5, 6), (6, 6)]
``````