One solution which I find pretty intuitive is to start with all zeros, and change N of thems into ones. Then the problems becomes "get all the combinations of three distinct positions", which can be achieved by using combination() function from Algorithm::Combinatorics.
use feature 'say';
use Algorithm::Combinatorics qw(combinations);
my $length = 10;
my $ones = 2;
my $iter = combinations([0..$length-1], $ones);
while (my $positions = $iter->next)
my @data = (0,) x $length;
$data[$_] = 1 for @$positions;
say join "", @data;
Now for the matter of speed, if it's really that important you'll have to benchmark, but if you're going to print each string then print
is probably going to make the execution time of generating the string insignificant.