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));
    }
}