In how many ways can a man put 12 playing cards on top of each other?

To determine the number of ways a man can stack 12 distinct playing cards on top of each other, we can use the concept of **permutations**. Since each card is distinct and the order in which they are placed matters, the number of possible arrangements is given by the factorial of the number of cards. The factorial of a number \( n \), denoted as \( n! \), is the product of all positive integers up to \( n \). For 12 cards: \[ 12! = 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 479,\!001,\!600 \] **Therefore, there are \( 12! = 479,\!001,\!600 \) ways to stack the 12 playing cards.** Answer: There are 12 factorial (12!) possible ways to arrange the 12 playing cards.