C# lottery 6 from 49 algorithm

问题

I need to display odds to win with ten decimals if I play with just one variant, for six five and four numbers. For example I need to have this 0.0000000715 but I have this 0.0027829314 if I introduce 49,6,I. What is the problem?How can I make it work? I am a beginner and I don't know how i can obtain this 0.0000000715.

 class Program
{
    static void Main(string[] args)
    {
        int n = Convert.ToInt32(Console.ReadLine());
        int k = Convert.ToInt32(Console.ReadLine());
        string category = Console.ReadLine();
        switch (category)
        {
            case "I":
                calculate(n,k);
                break;
            case "II":
                calculate(n, k);
                break;
            case "III":
                calculate(n, k);
                break;
        }
    }
    static void calculate(int n, int k)
    {
        int nk = n - k;
       decimal count = prod(1, nk) / prod(k + 1, n);
        decimal r = prod(1, k) / prod(n - k + 1, n);
        decimal sum = count * r;
        Console.WriteLine(Math.Round(r,10));
    }

    static decimal prod(int x, int y)
    {
        decimal prod = 0;
        for(int i = x; i <= y; i++)
        {
            prod = x * y;
        }
        return prod;
    }
}

回答1:

The general solution would be bc(6,n)*bc(49-6,6-n)/bc(49, 6), where n is, 4, 5 or 6 and bc is the binomial coefficient.

Btw.: double should be enough for 10 decimal places, there is no need to use decimal.

using System;       
public class Program
{
    //bonomial coefficient
    static double bc(double n, double k)  
    {
        if (k == 0 || k == n) 
            return 1;
        return bc(n - 1, k - 1) + bc(n - 1, k); 
    } 
    public static void Main()
    {
        for(int n = 4; n <=6; ++n){
            Console.WriteLine(bc(6,n)*bc(49-6,6-n)/bc(49, 6));
        }
    }
}

回答2:

I am not sur what function you were using.

The chances of winning all 6 numbers is 1 in 13,983,816

The actual calculation is this:

49C6 = 49!/(43! x 6!) = 13983816

So the probability to win is 1 / 13,983,816 = 0.0000000715

回答3:

Your prod function should look like:

 static decimal prod(int x, int y)
    {
        decimal prod = 1;
        for(int i = x; i <= y; i++)
        {
            prod = prod * i;
        }
        return prod;
    }

回答4:

As jjj mentioned, you overwrite "prod" everytime, but you need to add it

来源：https://stackoverflow.com/questions/63104134/c-sharp-lottery-6-from-49-algorithm

标签

algorithm