Raccoons!

namespace ManagedWorkspace
{
    using System;
    using System.Diagnostics;

    internal static class Program
    {
        private static void Main(string[] args)
        {
            int total_number_of_raccoons = 61;
            int total_number_of_tagged_raccoons = 8;
            Debug.Assert(total_number_of_raccoons >= total_number_of_tagged_raccoons);
            int total_number_of_untagged_raccoons = total_number_of_raccoons - total_number_of_tagged_raccoons;

            // p[n, k] = probability that k raccoons are tagged when chosen n raccoons.
            double[,] p = new double[total_number_of_raccoons + 1, total_number_of_tagged_raccoons + 1];

            // Simple base cases.
            p[1, 0] = ((double)total_number_of_untagged_raccoons) / total_number_of_raccoons;
            p[1, 1] = ((double)total_number_of_tagged_raccoons) / total_number_of_raccoons;

            for (int n = 2; n <= total_number_of_raccoons; n++)
            {
                for (int k = 0; k <= Math.Min(n, total_number_of_tagged_raccoons); k++)
                {
                    if (k == 0)
                    {
                        if (p[n - 1, k] > 0)
                        {
                            int number_of_raccoons_chosen = n - 1;
                            int number_of_tagged_raccoons_chosen = k;

                            int number_of_raccoons_remaining = total_number_of_raccoons - number_of_raccoons_chosen;
                            int number_of_tagged_raccoons_remaining = total_number_of_tagged_raccoons - number_of_tagged_raccoons_chosen;
                            int number_of_untagged_raccoons_chosen = number_of_raccoons_chosen - number_of_tagged_raccoons_chosen;
                            int number_of_untagged_raccoons_remaining = total_number_of_untagged_raccoons - number_of_untagged_raccoons_chosen;

                            Debug.Assert(number_of_raccoons_remaining >= 0);
                            Debug.Assert(number_of_tagged_raccoons_remaining >= 0);
                            Debug.Assert(number_of_untagged_raccoons_chosen >= 0);
                            Debug.Assert(number_of_untagged_raccoons_remaining >= 0);

                            p[n, k] = p[n - 1, k] * ((double)number_of_untagged_raccoons_remaining) / number_of_raccoons_remaining;
                        }
                    }
                    else if (k < n)
                    {
                        double A = 0;
                        double B = 0;
                        if (p[n - 1, k - 1]> 0)
                        {
                            int number_of_raccoons_chosen = n - 1;
                            int number_of_tagged_raccoons_chosen = k - 1;

                            int number_of_raccoons_remaining = total_number_of_raccoons - number_of_raccoons_chosen;
                            int number_of_tagged_raccoons_remaining = total_number_of_tagged_raccoons - number_of_tagged_raccoons_chosen;
                            int number_of_untagged_raccoons_chosen = number_of_raccoons_chosen - number_of_tagged_raccoons_chosen;
                            int number_of_untagged_raccoons_remaining = total_number_of_untagged_raccoons - number_of_untagged_raccoons_chosen;

                            Debug.Assert(number_of_raccoons_remaining >= 0);
                            Debug.Assert(number_of_tagged_raccoons_remaining >= 0);
                            Debug.Assert(number_of_untagged_raccoons_chosen >= 0);
                            Debug.Assert(number_of_untagged_raccoons_remaining >= 0);

                            A = ((double)number_of_tagged_raccoons_remaining) / number_of_raccoons_remaining;
                        }
                        if (p[n - 1, k] > 0)
                        {
                            int number_of_raccoons_chosen = n - 1;
                            int number_of_tagged_raccoons_chosen = k;

                            int number_of_raccoons_remaining = total_number_of_raccoons - number_of_raccoons_chosen;
                            int number_of_tagged_raccoons_remaining = total_number_of_tagged_raccoons - number_of_tagged_raccoons_chosen;
                            int number_of_untagged_raccoons_chosen = number_of_raccoons_chosen - number_of_tagged_raccoons_chosen;
                            int number_of_untagged_raccoons_remaining = total_number_of_untagged_raccoons - number_of_untagged_raccoons_chosen;

                            Debug.Assert(number_of_raccoons_remaining >= 0);
                            Debug.Assert(number_of_tagged_raccoons_remaining >= 0);
                            Debug.Assert(number_of_untagged_raccoons_chosen >= 0);
                            Debug.Assert(number_of_untagged_raccoons_remaining >= 0);

                            B = ((double)number_of_untagged_raccoons_remaining) / number_of_raccoons_remaining;
                        }
                        p[n, k] = p[n - 1, k - 1] * A + p[n - 1, k] * B;
                    }
                    else
                    {
                        double A = 0;
                        if (p[n - 1, k - 1] > 0)
                        {
                            int number_of_raccoons_chosen = n - 1;
                            int number_of_tagged_raccoons_chosen = k - 1;

                            int number_of_raccoons_remaining = total_number_of_raccoons - number_of_raccoons_chosen;
                            int number_of_tagged_raccoons_remaining = total_number_of_tagged_raccoons - number_of_tagged_raccoons_chosen;
                            int number_of_untagged_raccoons_chosen = number_of_raccoons_chosen - number_of_tagged_raccoons_chosen;
                            int number_of_untagged_raccoons_remaining = total_number_of_untagged_raccoons - number_of_untagged_raccoons_chosen;

                            Debug.Assert(number_of_raccoons_remaining >= 0);
                            Debug.Assert(number_of_tagged_raccoons_remaining >= 0);
                            Debug.Assert(number_of_untagged_raccoons_chosen >= 0);
                            Debug.Assert(number_of_untagged_raccoons_remaining >= 0);

                            A = ((double)number_of_tagged_raccoons_remaining) / number_of_raccoons_remaining;
                        }
                        p[n, k] = p[n - 1, k - 1] * A;
                    }
                }
            }
            Console.WriteLine(p[20, 4]);
        }
    }
}