Choose the best answer to the following question. Explain your reasoning with one or more complete sentences.

Suppose that four​ 6-sided dice are tossed. How many outcomes are​ possible?

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Part 1

Choose the correct answer below.

A.

6 times 6 times 6 times 66×6×6×6​, 

because each of the four dice have six possible outcomes.

B.

4 times 4 times 4 times 4 times 4 times 44×4×4×4×4×4​, 

because each of the six possible outcomes could appear on any of the four dice.

C.

​6, because each of the four dice have six possible outcomes.

D.

​6, because each of the six possible outcomes could appear on any of the four dice.

The correct answer is:

**A. 6 × 6 × 6 × 6, because each of the four dice have six possible outcomes.**

### Explanation:
Each die has 6 faces, meaning it can land on any one of 6 numbers (1 through 6). Since each die's outcome is independent of the others, the total number of possible outcomes for 4 dice is calculated by multiplying the number of outcomes for each die. Therefore, you multiply 6 (the number of outcomes for one die) by itself 4 times:

\[
6 \times 6 \times 6 \times 6 = 6^4 = 1296
\]

Thus, there are 1296 possible outcomes when four 6-sided dice are tossed.

### Incorrect Answers:
- **B** incorrectly multiplies 4 repeatedly, which is not correct because each die has 6 possible outcomes, not 4.
- **C** and **D** incorrectly state that the total number of outcomes is just 6, which overlooks the fact that there are 4 independent dice rolls.

Would you like more details or have any questions?

### Related Questions:
1. How many possible outcomes are there when 5 six-sided dice are rolled?
2. What is the probability of rolling four six-sided dice and getting exactly two 6’s?
3. How does the number of outcomes change if you roll 4 eight-sided dice instead of six-sided dice?
4. What is the probability of getting the same number on all four dice?
5. How would the total outcomes change if the dice were not independent?

### Tip:
When calculating outcomes for independent events, always multiply the number of possibilities for each event.

Suppose that four 6-sided dice are tossed. How many outcomes are possible? Choose the best answer from the following options: A. 6 × 6 × 6 × 6, because each of the four dice have six possible outcomes. B. 4 × 4 × 4 × 4, because each of the six possible outcomes could appear on any of the four dice. C. 6, because each of the four dice have six possible outcomes. D. 6, because each of the six possible outcomes could appear on any of the four dice.

Learn how to calculate the total number of possible outcomes when rolling four 6-sided dice. This problem uses basic combinatorics and the Fundamental Principle of Counting to explain how the number of outcomes is 6 × 6 × 6 × 6, resulting in 1296 possible combinations. Suitable for students in Grades 6-8.

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