sub get_key { join '', sort $_[0] =~ /./g }

my %hash;
while (<DATA>) {
   chomp;
   $hash{get_key($_)}++;
}

use Data::Dumper;
print(Dumper(\%hash));

__DATA__
AB
AB
AB
AC
AC
BA
BA
BA
CA

##</code><code>##

$VAR1 = {
          'AC' => 3,
          'AB' => 6
        };

##</code><code>##

sub get_key { join '', sort $_[0] =~ /./g }

my %hash;
while (<DATA>) {
   chomp;
   $hash{$_}++;
}

my %fixed;
foreach my $key (keys %hash) {
   my $val = $hash{$key};
   $fixed{get_key($key)} += $val;
}

use Data::Dumper;
print(Dumper(\%fixed));

__DATA__
AB
AB
AB
AC
AC
BA
BA
BA
CA