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 elements in the event that an ace, a king, a queen, and a jack are chosen.

To calculate the number of ways to choose one card from each suit such that the cards chosen include an ace, a king, a queen, and a jack, follow these steps:

### Key Points:
1. There are 4 suits in a standard deck: spades, hearts, diamonds, and clubs.
2. The problem specifies that one card from each suit is chosen.
3. Each card (Ace, King, Queen, Jack) must come from a different suit.

### Steps:
1. **Assign suits to the cards**: 
   - There are \( 4! \) ways to assign a specific suit to each card (since there are 4 cards to assign and 4 suits).

2. **Choose the cards within the assigned suits**:
   - Once a suit is assigned to each card, there is only **1 way** to choose the specific Ace, King, Queen, or Jack for each suit.

Thus, the total number of outcomes is:

\[
4! = 4 \times 3 \times 2 \times 1 = 24
\]

### Final Answer:
There are **24 elements** in the event that an Ace, King, Queen, and Jack are chosen.

---

Do you have any questions or want further clarification? Here are some related questions to expand your understanding:

1. What is the total number of ways to choose any 4 cards, one from each suit, without restrictions?
2. How would the solution change if you needed only face cards (Jack, Queen, King) from specific suits?
3. What is the probability of selecting an Ace, King, Queen, and Jack in this game?
4. How does the result change if the cards are not required to come from different suits?
5. What would be the outcome if jokers were included in the deck?

**Tip**: When solving combinatorics problems, carefully break the problem into systematic steps to avoid overlooking constraints!

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 elements in the event that an ace, a king, a queen, and a jack are chosen.

Explore how to calculate the number of ways to choose an Ace, King, Queen, and Jack, one from each suit, in a lottery-style game. This combinatorics problem demonstrates the application of permutations and factorials, suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation