SELECT department, count(department)
  FROM table
  GROUP BY department

##</code><code>##

use strict;

my %testhash = ( 8172263 => { name => 'Robert',
                              department => 'music' },
                 8177234 => { name => 'Elizabeth',
                              department => 'chemistry' },
                 7226331 => { name => 'Reginald',
                              department => 'chemistry' },
                 8117223 => { name => 'Ralph',
                              position => 'King' },
                 9118223 => { name => 'Richard',
                              department => 'music' },
                 9119233 => { name => 'Pamela',
                              department => 'music' }
                 );

# how do I discover the number of 
#   chemistry students in my hash very quickly?

my $musicstudents = grep { $testhash{$_}->{department} &&
                           $testhash{$_}->{department} =~ m/music/
                         }
                         keys %testhash;
print( "$musicstudents\n" );

##</code><code>##

   my %outputhash = somefunction(\%testhash, 'department');

##</code><code>##

  # my %outputhash = ( music => 3,
  #                    chemistry => 2 );

##</code><code>##

  my %outputhash;
  $outputhash{$_->{department}}++ for grep { $_->{department}
                                            } values %testhash;