How to implement a dealer class without storing a deck of cards?

Question

• Question

  Even only 52 cards, the permutationIndex where I describe in Explanations section, would be a huge number; it is

Answer 1

If I've understood you right, the following code implements this:

public class Dealer {
    public int Dealing() {
        var number=
            _freeCards.Count>0
                ?_freeCards.Dequeue()
                :_lastNumber++;

        _dealtCards.Add(number);
        return number;
    }

    public void Collect(int number) {
        if(!_dealtCards.Remove(number))
            throw new ArgumentException("Card is not in use", "number");

        _freeCards.Enqueue(number);
    }

    readonly HashSet _dealtCards=new HashSet();
    readonly Queue _freeCards=new Queue(); // "Pool" of free cards.
    int _lastNumber;
}