@places = Place.find(:all, :include => :categories, :conditions => { "categories_places.category_id" => id})

some_array_of_ids = [1, 2, 3]
@places = Place.find(:all, :include => :categories, :conditions => ['categories.id IN (?)', some_array_of_ids)

@places = Place.find(:all, :include => :categories, :conditions => ["categories_places.category_id IN ?", int])

some_array_of_ids = [1,2,3]
@places = Place.includes(:categories).where('categories.id IN (?)', some_array_of_ids)

some_array_of_ids = [1,2,3]
@places = Place.joins(:categories).where('categories.id': some_array_of_ids)

scope :by_categories, ->(category_ids) { joins(:categories).where('categories.id': category_ids) }

some_array_of_ids = [1,2,3]
@places = Place.by_categories(some_array_of_ids)