https://file.aiquickdraw.com/mathbot/file/1724773004494602mkm9i.jpg

The problem in the image reads:

"Sarah has some hats to wear. She will wear two hats of different color. She chooses between 3 red hats and 7 blue hats. In how many different ways can Sarah pair and wear a red hat and a blue hat?"

To solve this, let's break down the problem:

- Sarah has 3 red hats.
- Sarah has 7 blue hats.
- She needs to choose one red hat and one blue hat.

To find the total number of different combinations, we multiply the number of choices for the red hat by the number of choices for the blue hat:

\[
\text{Total combinations} = \text{Number of red hats} \times \text{Number of blue hats} = 3 \times 7 = 21
\]

So, there are 21 different ways Sarah can pair and wear a red hat and a blue hat.

Would you like more details or have any questions?

Here are some related questions you might consider:
1. What if Sarah had 5 red hats and 8 blue hats?
2. How would the number of combinations change if Sarah could choose hats of the same color?
3. What if Sarah wanted to wear two hats of any color combination?
4. How would the problem change if Sarah had an additional green hat option?
5. How can you generalize the formula for different numbers of hat colors?

**Tip:** When solving problems involving combinations, identify how many choices are available for each item and then multiply those choices.

Explore how to solve the problem of pairing red and blue hats using combinatorial principles. Sarah has 3 red hats and 7 blue hats. Learn the multiplication principle for counting and find out how many ways Sarah can pair and wear a red hat and a blue hat. Suitable for students in Grades 4-6.

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