(ns rlm.jen)

 

 (defn select-cells [n total-groups]

   (map (fn [_] (int (* total-groups (Math/random)))) (range n)))

 

 (defn all-selected? [selections n] 

   (= n (count (set selections))))

 

 (defn probability-of-all-selected

   [n desired total-groups total-trials]

   (let [trials

         (map (fn [_]

                (all-selected?

                 (select-cells n total-groups) desired))

              (range total-trials))

         prob

         (/ (count (filter identity trials)) total-trials)]

     prob))

 

 (defn your-problem [up-to trials-per-test]

   (print "selections       probability of getting all 15\n")

   (dorun

    (map

     (fn [n]

       (let [prob

             (probability-of-all-selected

              n 15 15 trials-per-test)]

         (printf "%10d             %1.3f\n" n (float prob))))

     (range up-to))))

 

 

 ;; rlm.jen> (your-problem 100 1000)

 ;; selections       probability of getting all 15

 ;;          0             0.000

 ;;          1             0.000

 ;;          2             0.000

 ;;          3             0.000

 ;;          4             0.000

 ;;          5             0.000

 ;;          6             0.000

 ;;          7             0.000

 ;;          8             0.000

 ;;          9             0.000

 ;;         10             0.000

 ;;         11             0.000

 ;;         12             0.000

 ;;         13             0.000

 ;;         14             0.000

 ;;         15             0.000

 ;;         16             0.000

 ;;         17             0.000

 ;;         18             0.001

 ;;         19             0.000

 ;;         20             0.001

 ;;         21             0.004

 ;;         22             0.005

 ;;         23             0.012

 ;;         24             0.008

 ;;         25             0.028

 ;;         26             0.031

 ;;         27             0.049

 ;;         28             0.045

 ;;         29             0.056

 ;;         30             0.100

 ;;         31             0.113

 ;;         32             0.125

 ;;         33             0.159

 ;;         34             0.152

 ;;         35             0.203

 ;;         36             0.216

 ;;         37             0.259

 ;;         38             0.285

 ;;         39             0.283

 ;;         40             0.331

 ;;         41             0.371

 ;;         42             0.420

 ;;         43             0.421

 ;;         44             0.456

 ;;         45             0.491

 ;;         46             0.527

 ;;         47             0.558

 ;;         48             0.534

 ;;         49             0.568

 ;;         50             0.580

 ;;         51             0.605

 ;;         52             0.668

 ;;         53             0.676

 ;;         54             0.678

 ;;         55             0.706

 ;;         56             0.726

 ;;         57             0.732

 ;;         58             0.743

 ;;         59             0.755

 ;;         60             0.761

 ;;         61             0.789

 ;;         62             0.804

 ;;         63             0.798

 ;;         64             0.837

 ;;         65             0.825

 ;;         66             0.832

 ;;         67             0.865

 ;;         68             0.871

 ;;         69             0.880

 ;;         70             0.894

 ;;         71             0.892

 ;;         72             0.892

 ;;         73             0.903

 ;;         74             0.911

 ;;         75             0.917

 ;;         76             0.926

 ;;         77             0.937

 ;;         78             0.922

 ;;         79             0.942

 ;;         80             0.927

 ;;         81             0.936

 ;;         82             0.952

 ;;         83             0.952

 ;;         84             0.960

 ;;         85             0.973

 ;;         86             0.969

 ;;         87             0.952

 ;;         88             0.963

 ;;         89             0.973

 ;;         90             0.971

 ;;         91             0.969

 ;;         92             0.980

 ;;         93             0.968

 ;;         94             0.975

 ;;         95             0.991

 ;;         96             0.980

 ;;         97             0.977

 ;;         98             0.982

 ;;         99             0.988

 ;; nil