package Maths;

/**
 * @see <a href="https://en.wikipedia.org/wiki/Combination">Combination</a>
 */
public class Combinations {
 public static void main(String[] args) {
 assert combinations(1, 1) == 1;
 assert combinations(10, 5) == 252;
 assert combinations(6, 3) == 20;
 assert combinations(20, 5) == 15504;
 }

 /**
 * Calculate of factorial
 *
 * @param n the number
 * @return factorial of given number
 */
 public static long factorial(int n) {
 if (n < 0) {
 throw new IllegalArgumentException("number is negative");
 }
 return n == 0 || n == 1 ? 1 : n * factorial(n - 1);
 }

 /**
 * Calculate combinations
 *
 * @param n first number
 * @param k second number
 * @return combinations of given {@code n} and {@code k}
 */
 public static long combinations(int n, int k) {
 return factorial(n) / (factorial(k) * factorial(n - k));
 }
}