...
#use List::Util 'shuffle';
use List::Util 'sample';
...
#my @playlist = (shuffle @all_files)[0 .. $list_length - 1];
my @playlist = sample $list_length, @all_files;
#print "$_\n" for sort @playlist;
print "$_\n" for @playlist;
...

##</code><code>##

ken@titan ~/tmp/pm_11150231_dir_rand_select
$ ./rand_select_files_sample.pl
/home/ken/tmp/pm_11150231_dir_rand_select/inc2/n.x
/home/ken/tmp/pm_11150231_dir_rand_select/a.x
/home/ken/tmp/pm_11150231_dir_rand_select/c.z

ken@titan ~/tmp/pm_11150231_dir_rand_select
$ ./rand_select_files_sample.pl
/home/ken/tmp/pm_11150231_dir_rand_select/inc1/j.z
/home/ken/tmp/pm_11150231_dir_rand_select/c.z
/home/ken/tmp/pm_11150231_dir_rand_select/inc1/h.x

ken@titan ~/tmp/pm_11150231_dir_rand_select
$ ./rand_select_files_sample.pl
/home/ken/tmp/pm_11150231_dir_rand_select/inc1/j.z
/home/ken/tmp/pm_11150231_dir_rand_select/c.z
/home/ken/tmp/pm_11150231_dir_rand_select/a.x