The function to generate all binary numbers was shown in the solution to the Perl Weakly Challenge 049. Iterate its results and use tr to count the occurrences of ones: 
#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

sub increment {
    my $pos = rindex $_[0], 0;
    if ($pos > -1) {
        substr $_[0], $pos, 1, '1';
        substr $_[0], $pos + 1, length($_[0]) - $pos - 1,
                         '0' x (length($_[0]) - $pos - 1);
    } else {
        $_[0] = '1' . ('0' x length $_[0]);
    }
}

my $ones = 3;
my $length = 10;
my $n = '0' x $length;
while ($length == length $n) {
    increment($n);
    next unless $ones == $n =~ tr/1//;
    say $n;
}

[download]

map{substr$_->[0],$_->[1]||0,1}[\*||{},3],[[]],[ref qr-1,-,-1],[{}],[sub{}^*ARGV,3]

In reply to Re: Generate all unique combinations of 1 and 0 using specified length of "0"-string and count of 1's by choroba
in thread Generate all unique combinations of 1 and 0 using specified length of "0"-string and count of 1's by Lana

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