toppings.clj

(defn factorial [n]
 (loop [iter n, res 1]
  (cond
   (zero? iter) res
   :else (recur (dec iter) (* res iter)))))

(defn combination [n k]
 (/ (factorial n) (* (factorial (- n k)) (factorial k))))

(comment k = number of hot dogs)
(comment n = number of toppings)
(comment Doesn't count the plain case)
(defn number-of-combinations [n k]
 (* (reduce + (map combination (repeat n n) (range n))) k))