gistfile1.rb

Enrollment.count(
  :select => "enrollments.course_id || ':' || enrollments.user_id",
  :distinct => true,
  :joins => :course,
  :group => "enrollments.type",
  :conditions => ["
    enrollments.course_id = courses.id AND
    enrollments.root_account_id = 2 AND
    courses.enrollment_term_id = 5 AND
    enrollments.role_name IS NULL AND
    enrollments.workflow_state != 'deleted' AND
    courses.sis_source_id IS NOT NULL
    "]
)

gistfile2.rb

# results
{"DesignerEnrollment"=>146, "ObserverEnrollment"=>7, "StudentEnrollment"=>6964, "StudentViewEnrollment"=>55, "TaEnrollment"=>63, "TeacherEnrollment"=>291}