Number of hands of poker
Poker users a 52-card deck, where each card is unique. After shuffling, a player gets five random cards. How many different hands are there? Remember, in poker, the order of the cards in your hand does not matter.
Write a function that takes the number of cards in a hand h and the number of cards in the deck d and calculates how many possible hands there are.
(defn combinations [d h]
.....
)Hint: there is a mathematical formula for combinations already!
| (defn factorial [n] | |
| (reduce * (range 1N (inc n)))) | |
| (defn combinations [deck hand] | |
| (let [d! (factorial deck) | |
| h! (factorial hand)] | |
| (/ d! (* h! (factorial (- deck hand)))))) |
| (ns deck-combinations | |
| (:require [clojure.test :refer :all])) | |
| (defn factorial [x] | |
| "Calculates the factorial of a number. Casts as a BigInteger upon integer overflow" | |
| (reduce *' (range 1 (inc x)))) | |
| (defn combinations [d h] | |
| (/ (factorial d) (* (factorial h) (factorial (- d h))))) | |
| ;; TESTS | |
| (deftest hand-combinations-test | |
| (is (= 1 (combinations 5 5))) | |
| (is (= 2598960 (combinations 52 5)))) |
| (defn combinations [d h] | |
| (assert (int? d)) | |
| (assert (int? h)) | |
| (assert (pos? h)) | |
| (assert (> d h)) | |
| (let [s (- d h) [b t] (sort [h s])] | |
| (loop [u (inc t) l b acc 1] | |
| (if (zero? l) | |
| acc | |
| (recur (inc u) (dec l) (/ (* acc u) l)))))) | |
| => #'user/combinations | |
| (combinations 10 8) | |
| => 45N | |
| (combinations 10 2) | |
| => 45N | |
| (combinations 52 5) | |
| => 2598960N |
| (defn fac [n] | |
| (reduce *' (range 1 (inc n)))) | |
| (defn combinations | |
| "possible hands of h cards from deck size d" | |
| [d h] | |
| (int (/ (fac d) (*' (fac h) (fac (- d h)))))) | |
| (combinations 52 5) ;; 52 card deck | |
| ;; 2598960 | |
| (combinations 52 7) ;; 7 cards | |
| ;; 20358520 | |
| (combinations 104 5) ;; 2 decks | |
| ;; 91962520 |
| (defn fact [n] (reduce * (range (bigint 1) (bigint (+ n 1))))) | |
| (defn combs [deck choose] (/ (fact deck) (* (fact choose) (fact (- deck choose))))) | |
| (combs 52 5) | |
| 2598960N |
| (defn fact [n] | |
| (reduce *' (range 1 (inc n)))) | |
| ;; Number of combinations of size 'n' taken from | |
| ;; a total collection of size 'pool-size'. | |
| (defn n-combinations [pool-size n] | |
| (/ (fact pool-size) | |
| (*' (fact n) | |
| (fact (- pool-size n))))) | |
| (def num-poker-hands (n-combinations 52 5)) ; => 2598960 |
| (defn factorial [n] (apply *' (map inc (range n)))) | |
| (defn combinations [d h] (/ (factorial d) (*' (factorial h) (factorial (-' d h))))) |
