C# 一个数组 每次取指定个数，不遗漏，不能重复，有多少种组合

背景：

C#  1到10的数组每次取三个不能重复，有多少种组合？{1,2,3,4,5,6,7,8,9,10}
比如1,2,3    1,2,4    1,2,5 等

求算法输出，，给出如下  已验证

 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp2
{
    class Program
    {
        static void Main(string[] args)
        {

            Int32[] arr = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
            String[] list = GetAllCombination(arr, 2);
            foreach (String s in list)
            Console.WriteLine(s);
            Console.WriteLine("组合总数：" + list.Length);

    }


        public static String[] GetAllCombination(Int32[] arr, Int32 n)  //取n个的组合 
        {
            Int32[] state = new Int32[arr.Length];
            List<String> list = new List<String>();

            for (Int32 i = 0; i < n; i++)
            {
                state[i] = 1;
            }
            for (Int32 i = n; i < state.Length; i++)
            {
                state[i] = 0;
            }

            String str = "";
            for (Int32 i = 0; i < n; i++)
                str += arr[i] + ",";

            list.Add(str.TrimEnd(','));

            while (true)
            {
                Boolean flag = true;
                Int32 index = 0;
                Int32 oneCount = 0;
                Int32 zeroCount = 0;
                StringBuilder sbuilder = new StringBuilder();

                for (; index < state.Length - 1; index++)
                {
                    if (state[index] == 1 && state[index + 1] == 0)
                    {
                        Int32 temp = state[index];
                        state[index] = state[index + 1];
                        state[index + 1] = temp;
                        break;
                    }
                }

                for (Int32 i = 0; i < index; i++)
                {
                    if (state[i] == 0)
                        zeroCount++;
                    else
                        oneCount++;
                }

                for (Int32 i = 0; i < index; i++)
                {
                    if (i < oneCount)
                        state[i] = 1;
                    else
                        state[i] = 0;
                }

                for (Int32 i = 0; i < arr.Length; i++)
                {
                    if (state[i] == 1)
                        sbuilder.Append(arr[i] + ",");
                }

                list.Add(sbuilder.ToString().TrimEnd(','));

                for (Int32 i = 0; i < arr.Length - n; i++)
                {
                    if (state[i] == 1)
                    {
                        flag = false;
                        break;
                    }
                }
                if (flag)
                    break;
            }

            return list.ToArray();
        }





    }
}