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- Derangements with repetitive numbers 1 answer
There is a card game I've played before, where it goes as follows:
You take a standard deck of cards, and shuffle them randomly. You then proceed by flipping each card and placing them down, simultaneously you count of ace, two, three, .. , queen, king, ace(2), two(2), three(3),...., king(4). That is you go through all 52 cards.
You lose the game only if the card that you read off is the same card as you were counting to. (i.e. the sequence two, ace, seven, four would lose at four.) Whereas, seven, four, two, king, queen, two, ace, eight would lose at the eight).
My question is how many possibilities are there to win this game? Also, how many possibilities are there to lose this game?