Trying to only list the faculty who have a specific specialization ( search by slug ) so if slug == nursing it only pulls up the faculty that has that specialization

faculty.rb

class Faculty < ApplicationRecord
  has_many :faculty_specializations
  has_many :specializations, through: :faculty_specializations
  extend FriendlyId
  friendly_id :meta_slug, use: :slugged
  has_one_attached :profile
end

faculty_specialization.rb

class FacultySpecialization < ApplicationRecord
  belongs_to :faculty
  belongs_to :specialization
end

irb.rb

Faculty.find(4).specializations
[17] pry(#<SpecializationController>)> Faculty.find(4).specializations
  CACHE Faculty Load (0.0ms)  SELECT "faculties".* FROM "faculties" WHERE "faculties"."id" = $1 LIMIT $2  [["id", 4], ["LIMIT", 1]]
  ↳ (pry):18:in `show'
  CACHE Specialization Load (0.0ms)  SELECT "specializations".* FROM "specializations" INNER JOIN "faculty_specializations" ON "specializations"."id" = "faculty_specializations"."specialization_id" WHERE "faculty_specializations"."faculty_id" = $1  [["faculty_id", 4]]
  ↳ app/controllers/specialization_controller.rb:4:in `show'
=> [#<Specialization:0x00007fb2da73afe8 id: 2, title: "Staff", slug: "staff">, #<Specialization:0x00007fb2da73acc8 id: 4, title: "Director", slug: "director">, #<Specialization:0x00007fb2da73aa98 id: 5, title: "Nursing", slug: "nursing">]
[18] pry(#<SpecializationController>)> 

Specialization.joins(:faculties).where(slug: 'nursing')
  CACHE Specialization Load (0.0ms)  SELECT "specializations".* FROM "specializations" INNER JOIN "faculty_specializations" ON "faculty_specializations"."specialization_id" = "specializations"."id" INNER JOIN "faculties" ON "faculties"."id" = "faculty_specializations"."faculty_id" WHERE "specializations"."slug" = $1  [["slug", "nursing"]]
  ↳ app/controllers/specialization_controller.rb:4:in `show'
=> [#<Specialization:0x00007fb2e0582fb0 id: 5, title: "Nursing", slug: "nursing">,
 #<Specialization:0x00007fb2e0582e48 id: 5, title: "Nursing", slug: "nursing">,
 #<Specialization:0x00007fb2e0582d58 id: 5, title: "Nursing", slug: "nursing">,
 #<Specialization:0x00007fb2e0582c40 id: 5, title: "Nursing", slug: "nursing">]
  
# Why is it showing an array of specializations which include faculty_ids and not the actualy faculty_ids
  
  Specialization.joins(:faculties).where(slug: 'nursing').first.faculty_ids
    CACHE Specialization Load (0.0ms)  SELECT "specializations".* FROM "specializations" INNER JOIN "faculty_specializations" ON "faculty_specializations"."specialization_id" = "specializations"."id" INNER JOIN "faculties" ON "faculties"."id" = "faculty_specializations"."faculty_id" WHERE "specializations"."slug" = $1 ORDER BY "specializations"."id" ASC LIMIT $2  [["slug", "nursing"], ["LIMIT", 1]]
  ↳ (pry):62:in `show'
  CACHE  (0.0ms)  SELECT "faculties"."id" FROM "faculties" INNER JOIN "faculty_specializations" ON "faculties"."id" = "faculty_specializations"."faculty_id" WHERE "faculty_specializations"."specialization_id" = $1  [["specialization_id", 5]]
  ↳ (pry):62:in `show'
=> [4, 11, 30, 37]


 Faculty.joins(:specializations).where(title: 'nursing')
  CACHE Faculty Load (0.0ms)  SELECT "faculties".* FROM "faculties" INNER JOIN "faculty_specializations" ON "faculty_specializations"."faculty_id" = "faculties"."id" INNER JOIN "specializations" ON "specializations"."id" = "faculty_specializations"."specialization_id" WHERE "faculties"."title" = $1  [["title", "nursing"]]
  ↳ app/controllers/specialization_controller.rb:4:in `show'
=> []
 Faculty.joins(:specializations).where(slug: 'nursing')
  CACHE Faculty Load (0.0ms)  SELECT "faculties".* FROM "faculties" INNER JOIN "faculty_specializations" ON "faculty_specializations"."faculty_id" = "faculties"."id" INNER JOIN "specializations" ON "specializations"."id" = "faculty_specializations"."specialization_id" WHERE "faculties"."slug" = $1  [["slug", "nursing"]]
  ↳ app/controllers/specialization_controller.rb:4:in `show'
=> []

  

specialization.rb

class Specialization < ApplicationRecord
  has_many :faculty_specializations
  has_many :faculties, through: :faculty_specializations
  extend FriendlyId
  friendly_id :title, use: :slugged
  validates_uniqueness_of :title


end