A state lottery game consists of choosing one card from each of the four suits in a standard deck of playing cards. (There are 13 cards in each suit.)
Count the number of ways in which four cards, each of a different face value, can be chosen.
To count the number of ways in which four cards, each of a different face value, can be chosen, we will consider each step separately.
1. Choose one face value from the 13 available face values in the deck. There are 13 ways to do this.
2. Once a face value is chosen, we need to choose one card from the 4 suits corresponding to that face value. There are 4 ways to do this.
3. After one card is chosen, we are left with 12 face values and 3 suits of the chosen face value. We repeat steps 1 and 2 for the remaining three cards.
4. Therefore, the total number of ways in which four cards, each of a different face value, can be chosen is:
13 (ways to choose the first face value) * 4 (ways to choose the suit for the first face value) * 12 (ways to choose the second face value) * 3 (ways to choose the suit for the second face value) * 11 (ways to choose the third face value) * 2 (ways to choose the suit for the third face value) * 10 (ways to choose the fourth face value) * 1 (ways to choose the suit for the fourth face value).
This simplifies to:
13 * 4 * 12 * 3 * 11 * 2 * 10 * 1 = 13! / 9! = 13 * 12 * 11 * 10 = 15,120
So, there are 15,120 ways in which four cards, each of a different face value, can be chosen from a standard deck of playing cards.