Cameron is packing gear for a hike. There are 7 pairs of hiking boots and 7 backpacks to choose from. How many different sets of hiking gear can Cameron pack?

To determine how many different sets of hiking gear Cameron can pack, we need to consider the combinations of hiking boots and backpacks he can choose from.

Cameron has 7 pairs of hiking boots and 7 backpacks to choose from. For each pair of hiking boots, he can pair it with any of the 7 backpacks.

The total number of different sets of hiking gear is calculated by multiplying the number of choices for hiking boots by the number of choices for backpacks:

\[
7 \times 7 = 49
\]

So, Cameron can pack **49 different sets of hiking gear**.

Would you like more details or have any questions? Here are five related questions:

1. How would the number of sets change if there were 8 pairs of hiking boots and 7 backpacks?
2. If Cameron wanted to pick 2 different sets of hiking gear, how many ways could he do that?
3. What if Cameron had only 5 backpacks to choose from? How many sets could he pack then?
4. If Cameron decides to pack 2 pairs of boots and 1 backpack, how many different combinations can he create?
5. How does the total number of sets change if Cameron adds a second type of gear, like hats, to his packing options?

**Tip:** When calculating combinations of independent choices, multiply the number of options for each choice to find the total number of combinations.

Explore how many different sets of hiking gear Cameron can pack with 7 pairs of hiking boots and 7 backpacks. Understand the concept of combinations and the multiplication principle in combinatorics. Suitable for students in Grades 4-6.

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