Perhaps this:

$ perl -E 'say for  grep {@b = split //; $c = 0;  for $i (@b){$c++ if 
+$i}; $c == 3}  glob "{0,1}{0,1}{0,1}{0,1}{0,1}";'
00111
01011
01101
01110
10011
10101
10110
11001
11010
11100
[download]

Update: sorry, forget it, I had missed or forgotten that you don't want to iterate 0 .. N and then count the bits and then eliminate. Saw it just after having posted.