I'm aware that this may be someone's homework, but that may be a good reason to try to make it interesting for all parties. I made life-long friends in combo, what Dr. Jay Goldman at UMN called "fancy counting." He was proud that he had never compiled a computer program. I would have gotten twenty bucks if I could have gotten him to compile:

./1.permute.pl : permutations for 851:
  8,5,1
  8,1,5
  5,8,1
  5,1,8
  1,8,5
  1,5,8
$ cat 1.permute.pl
#!/usr/bin/perl -w
use 5.011;

use Algorithm::Combinatorics qw/permutations/;

die "Usage : $0 number" unless scalar @ARGV;

my @digits = split //, $ARGV[0];

my $iter = permutations( \@digits );
print "$0 : permutations for $ARGV[0]:\n";
while ( my $p = $iter->next ) {
  print "  " . join( ",", @$p ) . "\n";
}
$
[download]

I think reasonable people could disagree as to what the "next" permutation is. Is the underlying set the natural numbers? Left to right is big to small? I thought I would take a swing at the next method:

#!/usr/bin/perl -w
use 5.011;
# https://metacpan.org/pod/Algorithm::Combinatorics
# first method implemented by bliako
use Algorithm::Combinatorics qw/permutations/;

die "Usage : $0 number" unless scalar @ARGV;

my @digits = split //, $ARGV[0];

my $iter = permutations( \@digits );
print "$0 : permutations for $ARGV[0]:\n";
while ( my $p = $iter->next ) {
  print "  " . join( ",", @$p ) . "\n";
}

# try next method with hungarian symbols
#
use utf8;
my @Erdős = permutations(\@digits);
say "airdish is";
say "@Erdős";
use Data::Dump;
dd \@Erdős;
my @descending = sort { $b <=> $a } @Erdős;
say "descending is";
dd \@descending;

$ ./2.permute.pl 372
./2.permute.pl : permutations for 372:
  3,7,2
  3,2,7
  7,3,2
  7,2,3
  2,3,7
  2,7,3
airdish is
ARRAY(0x5621ec17ad00) ARRAY(0x5621ec17ae80) ARRAY(0x5621ec17aec8) ARRA
+Y(0x5621ec23e770) ARRAY(0x5621ec2d4d80) ARRAY(0x5621ec2d5158)
[[3, 7, 2], [3, 2, 7], [7, 3, 2], [7, 2, 3], [2, 3, 7], [2, 7, 3]]
descending is
[[2, 7, 3], [2, 3, 7], [7, 2, 3], [7, 3, 2], [3, 2, 7], [3, 7, 2]]
$
[download]

Ordering these could turn into a boondoggle pretty quickly. Update: the use of word "method" in this post was technically misleading/misguided, as no objects are created. The word "function" is correct.