Austin has three pairs of pants, one black, one navy & one tan.  He also has two polo shirts, one red & one purple.  If Austin randomly selects one pair of pants and one polo shirt from his wardrobe, how many different outfit combinations can he create? 

Use the counting principal to determine the number of points in the sample space

To determine how many different outfit combinations Austin can create using the counting principle, we multiply the number of options for each independent choice.

Austin has:
- **3 pairs of pants**: black, navy, and tan
- **2 polo shirts**: red and purple

By the counting principle, the total number of outfit combinations is:

\[
\text{Total combinations} = (\text{Number of pants}) \times (\text{Number of shirts}) = 3 \times 2 = 6
\]

Thus, Austin can create **6 different outfit combinations**.

These combinations are:
1. Black pants with red polo
2. Black pants with purple polo
3. Navy pants with red polo
4. Navy pants with purple polo
5. Tan pants with red polo
6. Tan pants with purple polo

Would you like any more details or explanations?

Here are 5 related questions to expand on this:

1. What if Austin had three shirts instead of two? How many combinations would there be?
2. If Austin adds a pair of gray pants to his wardrobe, how many combinations would he then have?
3. What if Austin randomly selects a pair of pants, a shirt, and a pair of shoes from three options? How many combinations?
4. How many combinations would there be if Austin wanted to wear a jacket, and he had two to choose from?
5. What if Austin had 4 pairs of pants and 3 shirts, how would the number of combinations change?

**Tip**: The counting principle works by multiplying the number of ways each independent event can occur. This principle can be extended to any number of items or categories!

Austin has three pairs of pants, one black, one navy & one tan. He also has two polo shirts, one red & one purple. If Austin randomly selects one pair of pants and one polo shirt from his wardrobe, how many different outfit combinations can he create?

Learn how to calculate the number of different outfit combinations Austin can create with 3 pairs of pants and 2 polo shirts using the counting principle. This step-by-step solution explains the concept of combinatorics, suitable for students in Grades 5-7.

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