Program.cs

static void Main(string[] args)
{
	var rand = new Random();

	int success = 0;
	for (int i = 0; i < 100000; ++i)
	{
		var arr = Shuffle(new List<int> { 0, 0, 0, 0, 0, 0, 1, 1, 1, 1 });
		int sum = 0;
		for (int j = 0; j < 3; ++j)
		{
			int pick = rand.Next(arr.Count);
			int n = arr[pick];
			arr.RemoveAt(pick);
			if (n == 1) sum++;
		}
		if (sum == 1) success++;
	}

	Console.WriteLine("{0}, {1}", success, 100000);
	Console.ReadKey();
}

static List<int> Shuffle(List<int> array)
{
	Random rand = new Random();
	var arr = new List<int>();
	for (int i = 0; i < array.Count; ++i)
	{
		arr.Add(array[rand.Next(i, array.Count - 1)]);
	}
	return arr;
}