Calculation on the possibility that there is two dealt card with the distance of 1 in the card game called 'The MInd'.

the-mind.clj

(def nnv
  (memoize
    (fn [n k]
      (cond
        (= k 0) 1
        (> (* 2 k) (+ 1 n)) 0
        (= (* 2 k) (+ 1 n)) 1
        :else (bigint
                (+ (nnv (dec n) k)
                   (nnv (dec (dec n)) (dec k))))))))

(defn ! [x]
  (reduce (comp bigint *)
          (range 1 (inc x))))

(defn c [n k]
  (/ (! n)
     (* (! k)
        (! (- n k)))))

(defn p [n k]
  (->> (/ (nnv n k)
          (c n k))
       (double)
       (- 1)))

; (p 100 18) => 0.9756332632583158