I've realized too late that that number is supposed to be free too, so you need recursion (or fake it).

For completeness:

use strict;
use warnings;
use 5.12.0;

my $len = 5;
my $max = $len - 1;

for my $p0 ( 0 .. $max ) {
    for my $p1 ( $p0+1 .. $max ) {
        for my $p2 ( $p1+1 .. $max ) {
            my $str = "0" x $len;
            substr $str, $p0, 1, '1';
            substr $str, $p1, 1, '1';
            substr $str, $p2, 1, '1';
            say "$str $p0 $p1 $p2";
        }
    }
}
[download]

C:/Perl_524/bin\perl.exe -w d:/tmp/pm/bitstrings.pl 
11100 0 1 2
11010 0 1 3
11001 0 1 4
10110 0 2 3
10101 0 2 4
10011 0 3 4
01110 1 2 3
01101 1 2 4
01011 1 3 4
00111 2 3 4

Compilation finished at Fri Sep 18 10:43:25
[download]