Many problems in probability require that we count the number of ways that a particular event can occur or the number of outcomes in the sample space. To do this, we need to use counting techniques. One such technique is called the Fundamental Counting Principle: in a sequence of events, the total possible number of ways all events can performed is the product of the possible number of ways each individual event can be performed.

**Initial Post:**

You just started a new job, and your company has paid for new work attire!  You are curious how many outfits you can create and use the Fundamental Counting Principle to find out.

Use the Virtual Dice Roller and roll two dice three times (or grab a pair of dice at home!).

Record the sum of the two dice for each virtual roll.

The first virtual roll is how many work shirts you have in your closet.

The second roll is how many pairs of work pants you have in your closet.

The third roll is how many pairs of work shoes you have in your closet.

Calculate and explain how many different ways can you dress every morning.  Show all calculations.

To solve this problem, we will use the **Fundamental Counting Principle**, which states that the total number of possible outcomes for a sequence of events is the product of the number of ways each individual event can occur.

### Steps to calculate the number of outfits:

1. **Roll the dice three times** to simulate how many shirts, pants, and shoes you have in your closet.
   - The **first roll** determines how many work shirts you have.
   - The **second roll** determines how many pairs of work pants you have.
   - The **third roll** determines how many pairs of work shoes you have.

2. **Sum of dice rolls**: Since we are rolling two dice at a time, the possible sums for each roll range from 2 to 12.

### Example:

Let's roll the virtual dice three times:

1. First roll (shirts): Sum of 6.
2. Second roll (pants): Sum of 9.
3. Third roll (shoes): Sum of 5.

So, you have:
- 6 shirts,
- 9 pairs of pants,
- 5 pairs of shoes.

### Applying the Fundamental Counting Principle:
The total number of different outfits is calculated by multiplying the number of choices for each category (shirts, pants, and shoes):

\[
\text{Total number of outfits} = (\text{number of shirts}) \times (\text{number of pants}) \times (\text{number of shoes})
\]

Substitute the values we obtained from the dice rolls:

\[
\text{Total number of outfits} = 6 \times 9 \times 5 = 270
\]

### Conclusion:
There are **270 different ways** to dress every morning, given the numbers from the virtual dice rolls.

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Would you like more details or have any questions about this calculation?

Here are five follow-up questions you can explore:

1. What would happen if you had rolled a different number of shirts, pants, or shoes?
2. How does the range of possible sums for dice rolls (2 to 12) affect your wardrobe options?
3. How would the total number of outfits change if you add one extra pair of shoes?
4. Can you describe a real-life scenario where the Fundamental Counting Principle is useful?
5. What if there were additional accessories like ties or belts, how would that change the calculation?

**Tip**: When using the Fundamental Counting Principle, always make sure each event is independent of the others!

Many problems in probability require that we count the number of ways that a particular event can occur or the number of outcomes in the sample space. To do this, we need to use counting techniques. One such technique is called the Fundamental Counting Principle: in a sequence of events, the total possible number of ways all events can be performed is the product of the possible number of ways each individual event can be performed. You just started a new job, and your company has paid for new work attire! You are curious how many outfits you can create and use the Fundamental Counting Principle to find out. Use the Virtual Dice Roller and roll two dice three times (or grab a pair of dice at home!). Record the sum of the two dice for each virtual roll. The first virtual roll is how many work shirts you have in your closet. The second roll is how many pairs of work pants you have in your closet. The third roll is how many pairs of work shoes you have in your closet. Calculate and explain how many different ways can you dress every morning. Show all calculations.

Learn how to calculate the number of possible outfit combinations using the Fundamental Counting Principle. Roll virtual dice to determine the number of shirts, pants, and shoes, and multiply these values to find the total number of different outfits. This step-by-step guide explains key concepts in probability and combinatorics for Grades 6-8.

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