# Non-Unique sets of n elements with replacement

**URL:** <https://discourse.julialang.org/t/non-unique-sets-of-n-elements-with-replacement/43579>\
**Category:** General Usage\
**Created:** [July 23, 2020, 6:57pm UTC](https://discourse.julialang.org/t/non-unique-sets-of-n-elements-with-replacement/43579 "2020-07-23T18:57:37Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![PT.303](https://avatars.discourse-cdn.com/v4/letter/p/3da27b/32.png) [@PT.303](https://discourse.julialang.org/u/PT.303)\
**Post date:** [July 23, 2020, 6:57pm UTC](https://discourse.julialang.org/t/non-unique-sets-of-n-elements-with-replacement/43579/1 "2020-07-23T18:57:37Z")

</div>

Given a vector v = [1,…,n], I am trying to compute all non-unique sets of k elements with replacement.

For example, v = [1, 2, 3, 4, 5] and k = 3: should result in [1,1,1], [1,1,2], [1,1,3], [1,1,4], [1,1,5], [1,2,1], [1,2,2], [1,2,3], [1,2,4], [1,2,5], [1,3,1], [1,3,2], [1,3,3]… [5,5,4], [5,5,5]. With non-unique, I mean that if [1,1,2] is a solution, any of its permutations [1,2,1], [2,1,1] are as well.

I originally wrote the following code that outputted the correct solution:

all\_combinations = [[a, b, c, d, e] for a in min:max

```
                                                  for b in min:max

                                                  for c in min:max

                                                  for d in min:max

                                                  for e in min:max]

```

But I am now looking to do this for a variable number elements (n) and a variable combination size (k), [a, b, c, d, e, f, g] for example where k = 7 in this case and n=2 would yield [1,2] as a solution.

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<div class="post-metadata">

**Author:** ![Syx\_Pek](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/syx_pek/32/6364_2.png) [@Syx\_Pek](https://discourse.julialang.org/u/Syx_Pek)\
**Post date:** [July 23, 2020, 7:40pm UTC](https://discourse.julialang.org/t/non-unique-sets-of-n-elements-with-replacement/43579/2 "2020-07-23T19:40:19Z")

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```julia
function samplewithreplacement(set, copies)
  Iterators.product(repeat([set],copies)...)
end

n = 7; k = 2;
all_combinations = collect(samplewithreplacement(1:n, k))

```

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<div class="post-metadata">

**Author:** ![PT.303](https://avatars.discourse-cdn.com/v4/letter/p/3da27b/32.png) [@PT.303](https://discourse.julialang.org/u/PT.303)\
**Post date:** [July 23, 2020, 8:25pm UTC](https://discourse.julialang.org/t/non-unique-sets-of-n-elements-with-replacement/43579/3 "2020-07-23T20:25:56Z")

</div>

Thank you!

Could you explain the significance of the “. . .”? What does this do in the ‘product’ function?

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<div class="post-metadata">

**Author:** ![Syx\_Pek](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/syx_pek/32/6364_2.png) [@Syx\_Pek](https://discourse.julialang.org/u/Syx_Pek)\
**Post date:** [July 24, 2020, 6:07am UTC](https://discourse.julialang.org/t/non-unique-sets-of-n-elements-with-replacement/43579/4 "2020-07-24T06:07:39Z")

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When given a list, for example `[a,b,c]`, `f([a,b,c]...)` will be considered as `f(a,b,c)`.

As `Iterators.product` take a vararg, rather than a list, this allows us to “splat” in the variables.