using System;

public class Program

{

    private static double Factorial(int value) {

      double result = 1.0;

​

      for (int i = 2; i <= value; ++i)

        result *= i;

​

      return result;

    }

​

    static double Combinations(int x, int y) {

      return Factorial(x) / Factorial(y) / Factorial(x - y);

    }       

​

    // a - all possible numbers in a lottery, say 49

    // t - all taken numbers, say 6 (so we have 6 from 49)

    // c - category: 1 - all numbers win; 2 - all numbers win except 1; 3 - all numbers win except 2

    private static double Chances(int a, int t, int c) {

       return Combinations(t, t - c + 1) *

              Combinations(a - t, c - 1) /

              Combinations(a, t);

    }   

    public static void Main()

    {

        // from 40 number we take 5 and have 4 (category 2) winning ones

        Console.WriteLine(Chances(40, 5, 2));

    }

}