Sorted Tuples without Filtering

Question

Say I have a list $L$ where the elements can be sorted into some canonical order. I want to use Tuples[L,m] but I only want the output lists to be sorted and without repetition at any level. What I've currently got is

pretup = Tuples[L, m];
nextup = Table[Sort[pretup[[i]]], {i, 1, Length[L]^m}];
nextup = DeleteDuplicates[nextup];
finaltup = {};
Do[If[Length[DeleteDuplicates[nextup[[i]]]] == Length[nextup[[i]]], 
  AppendTo[finaltup, nextup[[i]]]], {i, 1, Length[nextup]}]
finaltup

but this is very inefficient. It first constructs all the possible combinations, then sorts them, then filters out duplicate sublists, then filters out duplicates within the sublists. Is there a faster way to do this? If so, what is it?

Answer 1

The function you are looking for is: Subsets.

E.g. for a list with n=5 elements and tuples with m=3 elements (note, you should not use capitalized variable names as those are used by the system):

n = 5;
m = 3;
l = Range[n];
Subsets[l, {m}]