How to create a list of pairs from 1d list(s)?

Say I've got two 1-dimensional lists

A = {1,2,3}
B = {a,b,c}

How do I

1. create a list of all pairs from list A such that the result looks like {{1,2},{1,3},{2,3}}?


2. create a list of all pairs from lists A and B such that the result looks like {{1,a},{1,b},{1,c},{2,a},{2,b},{2,c},{3,a},{3,b},{3,c}}?

I would also need both options, one with no duplicates as above and one with duplicates, e.g. one where the result from case 1 also includes {{2,1},{3,1},{3,2}}.

Answer

Ad. 1

ordering not valid:

Subsets[A, {2}]

{{1, 2}, {1, 3}, {2, 3}}

or with ordering

Permutations[A, {2}]

Ad. 2

Outer[List, A, B]

{{{1, a}, {1, b}, {1, c}}, {{2, a}, {2, b}, {2, c}}, {{3, a}, {3, b}, {3, c}}}

or exactly

Outer[List, A, B] // Flatten[#, 1] &

 {{1, a}, {1, b}, {1, c}, {2, a}, {2, b}, {2, c}, {3, a}, {3, b}, {3, c}}