so here a recursive version with global variables (because I also wanted to provide a solution with two nested loops "faking" recursion, but gave up)

NB: it's optimized for the dual case, where it's easier to set 0s into a string full of 1s.

use 5.12.0;
use strict;
use warnings;
use Data::Dump qw/pp dd/;
use Test::More;


my $ones = 3;
my $len = 5;

my @res;
my ($zero,$one) = ('0','1');

# optimize dual case
if ($ones > $len/2) {
    ($zero,$one) = ($one,$zero);
    $ones = $len-$ones;
}

my $max = $len - 1;
our $str = $zero x $len;
our $level = 0;

rec(0);
pp \@res;


sub rec {
    local $level = $level + 1;
    my ($start) =@_;
    for my $idx ( $start .. $max ) {
        local $str = $str;
        substr $str, $idx, 1, $one;
        if ($level < $ones) {
            rec( $idx + 1 );
        } else {
            push @res, $str;
        }
    }
}
[download]

[
  "00111",
  "01011",
  "01101",
  "01110",
  10011,
  10101,
  10110,
  11001,
  11010,
  11100,
]
[download]