For "6 choose 3, with replacement", you can use catalog {
:
{3#<i.6
┌─────┬─────┬─────┬─────┬─────┬─────┐
│0 0 0│0 0 1│0 0 2│0 0 3│0 0 4│0 0 5│
├─────┼─────┼─────┼─────┼─────┼─────┤
│0 1 0│0 1 1│0 1 2│0 1 3│0 1 4│0 1 5│
├─────┼─────┼─────┼─────┼─────┼─────┤
...
You can take the reverse as the index of the above matrix (unraveled), feg:
(0 0 0) I.~ >,{3#<i.6
0
(0 1 0) I.~ >,{3#<i.6
6
(5 5 5) I.~ >,{3#<i.6
215
(4 5 1) I.~ >,{3#<i.6
175
175 { >,{3#<i.6
4 5 1
There are some relevant essays on combinations on jsoftware.com: Combination Index, Combinations and others.