One solution that comes to mind is to generate the list out-of-order then sort it into order.

@bar=sort {zc($a) <=> zc($b)} 
      permute([0..2],[0..2],[0..2],[0..2],[0..2]);

sub zc{
  my $arg=shift;
  my @a=split //,$arg;
  return (grep /0/,@a[0..1])+(grep /0/,@a[3..4]);
}
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This is shorter (lines-of-code wise) than the 16 loops you describe, but will run slower. You could build the same sort of idea into the algorithm by using a heap w/ the same sort rule, but the end result would be algorithmically equivalent performance wise.

Another approach (it is too late tonight for me to work this out completely): Assume that permute($a,$b,$c,$d,$e) takes array references as its arguments and returns a list of all the permutations of the elements of those lists. Also assume that the function nz takes a list reference and returns all non-zero elements of that list. Then what you want to do is call permute like this:

push @list,permute(nz($a),nz($b),$c,nz($d),nz($e));
push @list,permute([0],nz($b),$c,nz($d),nz($e));
push @list,permute(nz($a),[0],$c,nz($d),nz($e));
push @list,permute(nz($a),nz($b),$c,[0],nz($e));
push @list,permute(nz($a),nz($b),$c,nz($d),[0]);
push @list,permute([0],[0],$c,nz($d),nz($e));
etc...
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Basically the "16 loops" you describe above. There is a very definite pattern to how the arguments of permute are set up for each call. Now all that is left is to figure out how to generate that pattern.