A deck of n cards numbered through are to be turned over one a time. Before each card is shown you are to guess which card it will be. After making your guess, you are told whether or not your guess is correct but not which card was turned over. It turns out that the strategy that maximizes the expected number of correct guesses fixes a permutation of the cards, say 1, 2, ..., n, and then continually guesses until it is correct, then continually guesses until either it is correct or all cards have been turned over, and then continually guesses , and so on. Let denote the number of correct guesses yielded by this strategy. Determine P(G = k).