gistfile1.rb

courses = Course.all(:conditions => "root_account_id = 2 AND enrollment_term_id = 5 AND workflow_state != 'deleted'")
types = ['StudentEnrollment', 'TeacherEnrollment', 'TaEnrollment', 'DesignerEnrollment', 'ObserverEnrollment', 'StudentViewEnrollment']
total_enrollments = {}
types.each do |t|
  total_enrollments[t] = 0
end
courses.each do |c|
  enrollments = c.enrollments.count(:distinct => true, :group => 'enrollments.type', :select => 'users.id', :conditions => 'enrollments.role_name IS NULL')
  puts "#{c.id} #{enrollments}"
  enrollments.each do |type, num|
    total_enrollments[type] = (total_enrollments[type] + num)
  end
end

gistfile2.rb

# results
{"StudentEnrollment"=>7060, "TeacherEnrollment"=>339, "TaEnrollment"=>64, "DesignerEnrollment"=>182, "ObserverEnrollment"=>8, "StudentViewEnrollment"=>66}