Ensure uniform (ish) distribution with random number generation

static IEnumerable<T> GetItems<T>(IEnumerable<Queue<T>> queues)
{
    int remaining = queues.Sum(q => q.Count);
    Random rand = new Random();
    while (remaining > 0)
    {
        int index = rand.Next(remaining);
        foreach (Queue<T> q in queues)
        {
            if (index < q.Count)
            {
                yield return q.Dequeue();
                remaining--;
                break;
            }
            else
            {
                index -= q.Count;
            }
        }
    }
}

int remaining = 0;
foreach(Queue<T> q in queues) {remaining += q.Count;}

static void Main()
{
    List<Queue<int>> queues = new List<Queue<int>> {
        Build(1,2,3,4,5), Build(6,7,8), Build(9,10,11,12,13)
    };
    foreach (int i in GetItems(queues))
    {
        Console.WriteLine(i);
    }
}
static Queue<T> Build<T>(params T[] items)
{
    Queue<T> queue = new Queue<T>();
    foreach (T item in items)
    {
        queue.Enqueue(item);
    }
    return queue;
}

private Random random = new Random();
public int RandomSort(Queue q1, Queue q2)
{
  if (q1 == q2) { return 0; }
  return random.Next().CompareTo(random.Next());
}