Hi, I started learning clojure for a few months and this is what I have for 
the problem, and I find it running very slow if exceeding 100k trials, maybe 
it's because of using set?  Any feedbacks will be appreciated. thx

(require '[clojure.set :as set])
(def doors #{:a :b :c})
(defn rand-nth-set [s]
 (conj #{} (rand-nth (seq s))))

(defn play
  ([] (play nil))
  ([switch?]
   (let [prize-door  (rand-nth-set doors)
         picked-door (rand-nth-set doors)
         empty-doors (set/difference doors prize-door)
         opened-door (rand-nth-set (set/difference empty-doors picked-door))
         picked-door (if switch?
                       (set/difference doors opened-door picked-door)
                       picked-door)]
     (= picked-door prize-door))))

(count (remove #(false? %) (repeatedly 10000 #(play true))))
(count (remove #(false? %) (repeatedly 10000 #(play false))))


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