一道组合排列题

%52 正好有一双 书本后答案 0.4268 计算机模拟结果 0.4268
2*(factorial(8) * 2^6/(2)) * nchoosek(10,1)*nchoosek(9,6)/(20*19*18*17*16*15*14*13) %书上的差一倍

 

nchoosek(10,1)*18*16*14*12*10*8/(nchoosek(20,8) * factorial(6)) %分子分母按组合来取
%先取1双的组合数有10，然后再取6双的排列数，将排列数转乘组合数 是除以6!

56*nchoosek(10,1)*18*16*14*12*10*8/(20*19*18*17*16*15*14*13) %分子分母按排列数来取

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;
using System.Diagnostics;
namespace ConsoleApplication2
{
    class Program
    {
        static void Main(string[] args)
        {
            //Stopwatch sw = new Stopwatch();
            //sw.Start();
            T4();
            //sw.Stop();
            //Console.WriteLine(sw.ElapsedMilliseconds);
            Console.ReadLine();
        }

        private static void T1()
        {
            var list = new List<List<int>>();
            var count = 0;
            StringBuilder sb = new StringBuilder();
            for (int f1 = 1; f1 <= 6; f1++)
            {
                for (int f2 = 1; f2 <= 6; f2++)
                {

                    for (int f3 = 1; f3 <= 6; f3++)
                    {

                        for (int f4 = 1; f4 <= 6; f4++)
                        {

                            for (int f5 = 1; f5 <= 6; f5++)
                            {
                                var dic = new int[] { 0, 0, 0, 0, 0, 0, 0 };
                                dic[f1]++; dic[f2]++; dic[f3]++;
                                dic[f4]++; dic[f5]++;

                                var pcount = 0;
                                var tcount = 0;
                                foreach (int it in dic)
                                {
                                    if (it == 2)
                                    {
                                        pcount++;
                                    }
                                    if (it > 2)
                                    {
                                        tcount++;
                                    }
                                }
                                if (pcount == 2)
                                {

                                    var str = string.Format("{0}-{1}-{2}-{3}-{4}", f1, f2, f3, f4, f5);
                                    Console.WriteLine(str);
                                    sb.AppendLine(str);
                                    count++;
                                }
                            }
                        }
                    }
                }
            }
            File.WriteAllText(@"C:\jbs.txt", sb.ToString());
            Console.WriteLine(count);
            Console.WriteLine(count / Math.Pow(6, 5));
        }
        static void T4()
        {
            var shope = new List<String>();
              #region 10双鞋
            for(int i = 0; i < 10; i++)
            {
                 byte av=(byte)(65+i);
                 var no=Encoding.ASCII.GetString( new byte[]{av} );
                 shope.Add(no + "1");
                 shope.Add(no + "2");
                   
            }

             #endregion
            var rnd = new Random(Environment.TickCount);
            var mCount = 0;
            var total = 10000000;
            for (int tIndex = 0; tIndex < total; tIndex++)
            {
                #region 随机拿8双
                var getSet = new List<String>();
                while (getSet.Count < 8)
                {
                    var index = rnd.Next(20);
                    if (getSet.Contains(shope[index])) continue;
                    getSet.Add(shope[index]);

                }
                #endregion
                #region 检测刚好一双的
                var olist = getSet.OrderBy(ent => ent).ToList();
                var prev = "9";
                var pc = 0;
                for (int i = 0; i < olist.Count; i++)
                {
                    var cur = olist[i].Substring(0, 1);
                    if (cur == prev)
                    {
                        pc++;

                    }
                    prev = cur;
                }
                if (pc == 1)
                {
                    mCount++;
                    
                    //olist.ForEach(ent => Console.Write(ent + "-"));
                    //Console.WriteLine();

                }
                #endregion
            }
            Console.WriteLine("共计:" + mCount +"/" + total);
            Console.WriteLine("概率:" + (double)mCount / (double)total);

        }
        static void T3()
        {
            var AT = new string[] { "A", "B", "C", "D", "E" ,"F","G","H"};
            int count = 0;
            var dic = new Dictionary<string, int>();
            
            for (int f1 = 0; f1 < 8; f1++)
            {
                for (int f2 = 0; f2 < 7; f2++)
                {
                    for (int f3 = 0; f3 < 6; f3++)
                    {
                        for (int f4 = 0; f4 < 5; f4++)
                        {
                            for (int f5 = 0; f5 < 4; f5++)
                            {
                                for (int f6 = 0; f6 < 3; f6++)
                                {
                                    for (int f7 = 0; f7 < 2; f7++)
                                    {
                                        for (int f8 = 0; f8 < 1; f8++)
                                        {
                                            var list = new List<String>(AT);
                                            var k1 = list[f1]; list.RemoveAt(f1);
                                            var k2 = list[f2]; list.RemoveAt(f2);
                                            //ChangeIfGreater(ref k1, ref k2);
                                            var k3 = list[f3]; list.RemoveAt(f3);
                                            var k4 = list[f4]; list.RemoveAt(f4);
                                            ChangeIfGreater(ref k3, ref k4);
                                            var k5 = list[f5]; list.RemoveAt(f5);
                                            var k6 = list[f6]; list.RemoveAt(f6);
                                            ChangeIfGreater(ref k5, ref k6);
                                            var k7 = list[f7]; list.RemoveAt(f7);
                                            var k8= list[f8]; list.RemoveAt(f8);
                                            ChangeIfGreater(ref k7, ref k8);
                                            var tmp = string.Format("{0},{1},{2}-{3},{4}-{5},{6}-{7}", k1, k2, k3, k4, k5,k6,k7,k8);
                                            if (!dic.ContainsKey(tmp))
                                            {
                                                dic[tmp] = 0;
                                                Console.WriteLine(tmp);
                                                count++;
                                            }
                                            dic[tmp]++;

                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
            var sb = new StringBuilder();
            foreach (var v in dic.Keys)
            {
                if(v.IndexOf("C-D")<0)continue;
                if(v.IndexOf("E-F")<0)continue;
                if (v.IndexOf("G-H") < 0) continue;
                sb.AppendLine(v);
            }
            File.WriteAllText(@"C:\kjbs.txt",sb.ToString());
            Console.WriteLine(count);
        }
        static void ChangeIfGreater(ref string v1, ref string v2)
        {
           
            if (string.Compare(v1,v2)>0)
            {
                var tmp = v1;
                v1 = v2;
                v2 = tmp;

            }
        }
        static void T2()
        {
            var Arr = new int[] { 1, 1, 2, 2, 3 };
            var AT = new string[] { "A", "B", "C", "D", "E" };
            var count = 0;
            var dic = new Dictionary<string, int>();
            var rList = new List<String>();
            for (int f1 = 0; f1 < 5; f1++)
            {
                for (int f2 = 0; f2 < 4; f2++)
                {
                    for (int f3 = 0; f3 < 3; f3++)
                    {
                        for (int f4 = 0; f4 < 2; f4++)
                        {
                            for (int f5 = 0; f5 < 1; f5++)
                            {
                                var list = new List<int>(Arr);
                                var k1 = list[f1]; list.RemoveAt(f1);
                                var k2 = list[f2]; list.RemoveAt(f2);
                                var k3 = list[f3]; list.RemoveAt(f3);
                                var k4 = list[f4]; list.RemoveAt(f4);
                                var k5 = list[f5]; list.RemoveAt(f5);
                                var tmp = string.Format("{0}-{1}-{2}-{3}-{4}", k1, k2, k3, k4, k5);
                                if (!dic.ContainsKey(tmp))
                                {
                                    dic[tmp] = 1;
                                    //Console.WriteLine(tmp);
                                    var arr1 = new int[] { k1, k2, k3, k4, k5 };
                                    var g1 = "";
                                    var g2 = "";
                                    var g3 = "";
                                    for (int i = 0; i < 5; i++)
                                    {
                                        var a = arr1[i];
                                        if (a == 1)
                                        {
                                            g1 += AT[i] + "-";
                                        }
                                        if (a == 2)
                                        {
                                            g2 += AT[i] + "-";
                                        }
                                        if (a == 3)
                                        {
                                            g3 += AT[i] + "-";
                                        }
                                    }
                                    if (string.Compare(g1, g2) > 0)
                                    {
                                        var tmp2 = g1;
                                        g1 = g2;
                                        g2 = tmp2;
                                    }

                                    var rStr = g1.Trim("-".ToCharArray()) + " "
                                                      + g2.Trim("-".ToCharArray()) + " "
                                                      + g3.Trim("-".ToCharArray());
                                    rList.Add(rStr);
                                    Console.WriteLine(rStr + "    :" + (count + 1));
                                    count++;

                                }
                                else
                                {
                                    dic[tmp]++;
                                }

                            }
                        }
                    }
                }
            }
            //foreach (var item in rList.OrderBy(ent => ent).ToList())
            //{
            //    Console.WriteLine(item);
            //}
            Console.WriteLine(count);
        }

        static void T5()
        {
            var arr = new List<int>();
            var person = 6;
            for (int i = 0; i < person; i++)
            {
                arr.Add(0);
            }
            Loop(0, person, arr, 0, 12);
        }
        static List<String> PersonBirthdayList = new List<string>();
        static void Loop(int level,int maxLevel, List<int> arr,int low,int high)
        {
            for (int i = low; i < high; i++)
            {
                arr[level] = i;
 
                if ( (level +1) < maxLevel)
                {
                    Loop(level + 1, maxLevel, arr, low, high);
                }
                else
                {
                    var line= arr.Aggregate("", (t, e) => t += "-" + e).Trim("-".ToCharArray());
                    PersonBirthdayList.Add(line);
                }
            }
        }

        static void T6()
        {

            var rnd = new Random(Environment.TickCount);

            var total = 90000000;
            var count = 0;

            for (int tIndex = 0; tIndex < total; tIndex++)
            {

                var person = new int[20];
                for (int i = 0; i < 20; i++)
                {
                    person[i] = rnd.Next(1, 13);
                }
                var p2 = 0;
                var p3 = 0;

                var g = person.GroupBy(ent => ent).ToList();
                foreach (var gitem in g)
                {
                    if (gitem.Count() == 2)
                    {
                        p2++;
                    }
                    if (gitem.Count() == 3)
                    {
                        p3++;
                    }
                }
                if (p2 == 4 && p3 == 4)
                {
                    count++;
                    string line = "";
                    for (int j = 0; j < person.Length; j++)
                    {
                        line += person[j] + "-";
                    }
                   // Console.WriteLine(line.Trim("-".ToCharArray()));
                }
            }
            Console.WriteLine(count);
            Console.WriteLine("共计:" + count + "/" + total);
            Console.WriteLine("概率:" + (double)count / (double)total);
        }
    }
}

 

注意分母如果是20*19*18*17*16*15*14*13是考虑顺序的排列时，那么分子部分也应该是需要考虑顺序的排列 直接按  C(10,1) 18*16*14*12*10*8,只考虑后面6双鞋的排序，

所以要把前面凑成一双的2只鞋补上去， 补第一只时，我们有7个位置可选，然后补第二只我们有8个位置可选，所以要乘以7*8=56

 

如果分母是 C(20,8) 是组合 那么需要“消除” 18*16*14*12*10*8 这6只鞋的排列数，也就是除以 6!