Multiple unique random samples?

Question

I'm trying to produce $n$ random samples from a list, but not all samples, and I'd like the samples to not repeat in the same execution of the command. If I'm not mistaken, something like Permutations[] for not all permutations, or RandomPermutation for a list, or a hypothetical MultipleRandomSample[]. Is there something I'm misinterpreting or a way to generate such collections of random samples?

Edit: What I'm calling random samples are actually subsets, since they are fixed size and order doesn't matter. Now, I only need to take $n$ random subsets from a set.

RandomSample repeats "subsets":

Table[RandomSample[{2, 3, 5, 8}, 3], 10]
{{3, 2, 5}, {5, 8, 2}, {8, 3, 2}, {8, 5, 2}, {2, 3, 5}, {8, 2, 3}, {2,
   3, 8}, {2, 5, 3}, {8, 3, 5}, {2, 8, 5}}

Subsets is adequate, but it gives all subsets, and I wish to find $n$ random subsets:

Subsets[{2, 3, 5, 8}, {3}]
{{2, 3, 5}, {2, 3, 8}, {2, 5, 8}, {3, 5, 8}}

A simulated result would be:

Table[Op[{2, 3, 5, 8}, {3}],3]
{{{2, 3, 5}, {2, 3, 8}, {2, 5, 8}},
{{2, 3, 5}, {2, 3, 8}, {3, 5, 8}},
{{2, 3, 8}, {2, 5, 8}, {2, 5, 8}},
{{2, 3, 8}, {2, 5, 8}, {2, 5, 8}}(*repetitions are ok*)}

Is there a way to produce such collections of subsets without obtaining all subsets, randomizing, and taking $n$?

Answer 1

You just need to use the 3-arg syntax for Subsets. Here is a function that does this:

MultipleRandomSubsets[list_, length_, count_] := Module[{total},
    total = Binomial[Length @ list, length];
    Join @@ Map[Subsets[list, {length}, {#}]&] @ RandomSample[1 ;; total, count] /; count <= total
]

Small example:

SeedRandom[1]
MultipleRandomSubsets[{2,3,5,8}, 3, 3]

{{3, 5, 8}, {2, 3, 8}, {2, 3, 5}}

An example that couldn't be done by enumerating all samples:

SeedRandom[1]
MultipleRandomSubsets[Range[100], 10, 10]

{{16, 23, 32, 33, 45, 49, 70, 72, 85, 92}, {17, 18, 31, 41, 43, 64, 80, 87, 88, 97}, {1, 13, 18, 37, 40, 43, 46, 48, 61, 88}, {5, 19, 22, 40, 43, 53, 58, 68, 73, 88}, {19, 28, 60, 76, 83, 85, 95, 96, 98, 99}, {9, 30, 32, 46, 53, 66, 77, 86, 89, 90}, {1, 9, 19, 20, 21, 28, 51, 76, 80, 96}, {9, 16, 22, 61, 67, 69, 79, 82, 98, 99}, {8, 34, 40, 43, 80, 82, 84, 87, 96, 98}, {13, 34, 38, 44, 47, 48, 49, 67, 74, 80}}

Answer 2

This is not an answer, but a request for clarification that can't be made in a comment.

I'm confused by your question because it seems to me to be open to several interpretations. Here are three that immediately occur to me.

Suppose that sample is a function, taking no argument, that will return a random sample meeting your requirements, and suppose that we use it to generate a set of samples. Note: it may be the sample can not be written — we might need to generate the whole sample set at once and not sample-by-sample — but we will assume it exists for the sake of discourse.

Sample generation

sampleSet = With[{n = 5}, Do[sample[], n]];

Now, which of the following, increasingly stringent requirements does sampleSet have to meet?

require[1] = Flatten[Intersection /@ sampleSet] == {}

require[2] = Intersection @@ sampleSet == {}

require[3] = Module[{smpl = Flatten[sampleSet]}, Sort[smpl] == Union[smpl]]

Or is it none of the above? If the latter, please state your requirements in Mathematica code.