Note that the string in question contains exactly once each of the integer 1, . . . , 5. Such a string is called a permutation of {1, . . . , 5} (i.e., of 5 objects). The name permutation comes from a dierent perspective which is also important to us. Namely, if we think of starting with the cards in order: 1 on top, 5 at the bottom, the string (3, 5, 2, 1, 4) tell us that the card originally in position 1 is now in position 4, the card originally in position 2 is now in position 3, the card originally in position 3 is now in position 1, the card originally in position 4 is now in position 5, the card originally in position 5 is now in position 2. That is, the string tells us how the cards have been permuted. # How many dierent decks of 3 cards are there? How many dierent decks of n cards are there?