use Algorithm::Permute qw(permute);

@a     = 'a' .. 'd';
$afact = 1;
$afact *= $_ for 2 .. @a;
permute {
    $h{ join '', sort { rand() < rand() } @a } += 1 / $afact;
} @a for 1 .. 1e5;   # a million takes a couple minutes

printf "$_ : %.2f%%\n", $h{ $_ } / 1e3 for sort keys %h;