type
  maska = array[1..8] of boolean;

const
  chars = '12345678';

var
  msk: maska;

procedure replaces(s: string; c: byte; m: maska);
var
  i: integer;
begin
  if c = 8 then
    Form1.Memo1.Lines.Add(s)
  else
    for i := 1 to 8 do
      if not m[i] then
        begin
          m[i] := true;
          replaces(s + chars[i], c+1, m);
          m[i] := false;
        end;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
  replaces('',0,msk);
end;