https://file.aiquickdraw.com/mathbot/file/1728451461154lhvj7emr.jpg

The question in the image asks: 

"If you buy four pairs of jeans, three sweaters, and three pairs of boots, how many new outfits (consisting of a new pair of jeans, a new sweater, and a new pair of boots) will you have?"

To calculate the total number of new outfits, we use the multiplication principle of counting (combinatorics). For each outfit, you will need one pair of jeans, one sweater, and one pair of boots. Since these items can be mixed and matched in any combination, the total number of outfits is the product of the number of jeans, sweaters, and boots.

\[
\text{Total outfits} = 4 \, (\text{jeans}) \times 3 \, (\text{sweaters}) \times 3 \, (\text{boots}) = 36
\]

So, you will have **36 new outfits**.

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

Here are 5 related questions to expand your understanding:
1. What happens if you have an additional clothing item like hats or scarves? How would that change the calculation?
2. If you had 5 pairs of jeans instead, how many outfits could you make?
3. How would the number of combinations change if you could also mix the same sweater with multiple jeans in a different outfit each day?
4. What if some of the items can only be paired with specific others (e.g., jeans with specific boots)?
5. How would you calculate this for an unlimited number of clothing items?

**Tip:** When dealing with combinations or outfits, the multiplication principle is very useful in counting how different groups can be mixed together.

If you buy four pairs of jeans, three sweaters, and three pairs of boots, how many new outfits (consisting of a new pair of jeans, a new sweater, and a new pair of boots) will you have?

Learn how to calculate the total number of outfit combinations with 4 pairs of jeans, 3 sweaters, and 3 pairs of boots. This combinatorics problem uses the multiplication principle to find that there are 36 possible unique outfits. Suitable for students in Grades 5-7.

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