I missed that "BA" in the list. The last page of Algorithm::Loops talks specifically about this problem and shows a few ways to do it. A fairly minor update to my code is one such way:

#!/usr/bin/perl -w
use strict;

use Algorithm::Loops qw( NestedLoops NextPermute );

my @items= ( 1..5 );
my $choose= 2;
my $iter= NestedLoops(
    [   [ 0..$#items ],
        ( sub { [ $_+1 .. $#items ] } ) x ($choose-1),
    ],
);
my @choice;
while(  @choice= @items[$iter->()]  ) {
    do {
        print "@choice\n";
        # replace above line with your code
    } while(  NextPermute(@choice)  );
}
[download]

produces

1 2
2 1
1 3
3 1
1 4
4 1
1 5
5 1
2 3
3 2
2 4
4 2
2 5
5 2
3 4
4 3
3 5
5 3
4 5
5 4
[download]