you can use this:

#!/usr/bin/perl -w
use strict;
use Data::Dumper;

# While matching the hash, elem of each array must occur together
# and in order

my @ar1   = ('A','B');      #Answer: 3
my @ar2   = ('B','A');      #Answer: 1
my @ar3   = ('A','B','C');  #Answer: 2

my $hash = {
            'S1' => [ 'A', 'B', 'C', 'A' ],
            'S2' => [ 'A', 'C', 'D', 'B' ],
            'S3' => [ 'C', 'A', 'D', 'H' ],
            'S4' => [ 'A', 'B', 'I', 'C' ]
           };

count_($hash,\@ar1);
count_($hash,\@ar2);

sub count_ {
  my ($hashref,$arref) = @_;
  my $counter = 0;
    my $test = join('.*?',@$arref);
  print "Query: ",join('',@$arref),"\n";
  for my $key(sort{$a cmp $b}keys(%$hashref)){
    my $string = join('',@{$hashref->{$key}});
    print $string," - ";
    if($string =~ $test){
      print "1\n";
      $counter++;
    }
    else{
      print "0\n";
    }
  }
  print "Total counter: ",$counter,"\n"
}# end count_
[download]

output:

Query: AB
ABCA - 1
ACDB - 1
CADH - 0
ABIC - 1
Total counter: 3
Query: BA
ABCA - 1
ACDB - 0
CADH - 0
ABIC - 0
Total counter: 1
[download]