排队买票-题解(Java代码)

为啥我这个是错的？
import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int M = sc.nextInt();
        int N = sc.nextInt();
        int K = sc.nextInt();
        System.out.println(f(N, K) * factorial(N) * factorial(K));
    }
    public static int f(int N, int K){
        if(N < K) return 0;
        if(K == 0)return 1;
        //从后往前排
        return f(N - 1, K) + f(N, K - 1);
    }
    public static int factorial(int n){
        if(n == 1)return 1;
        return n * factorial(n - 1);
    }
}