Question

fundamental counting principle

a student can choose from 12 types of backpacks, 5 pencil cases and 7 water bottles. how many school supply sets can they create?

number of sets = ?

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Fundamental Counting Principle"
],
"new_concepts": [],
"current_concepts": [
"Fundamental Counting Principle"
]
}
</pre_analysis>

<reasoning>

Identify the choices for each item

\[

$$\begin{aligned} &\text{Backpacks } (B) = 12 \\ &\text{Pencil cases } (P) = 5 \\ &\text{Water bottles } (W) = 7 \end{aligned}$$

\]

Apply the multiplication rule

\[

$$\begin{aligned} \text{Total Sets} &= B \times P \times W \\ &= 12 \times 5 \times 7 \\ &= 60 \times 7 \\ &= 420 \end{aligned}$$

\]
</reasoning>

<answer>
A student can choose from 12 types of backpacks, 5 pencil cases and 7 water bottles. How many school supply sets can they create?

Number of Sets = <blank>420</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Statistics",
"Fundamental Counting Principle"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Fundamental Counting Principle"
],
"new_concepts": [],
"current_concepts": [
"Fundamental Counting Principle"
]
}
</pre_analysis>

<reasoning>

Identify the choices for each item

\[

$$\begin{aligned} &\text{Backpacks } (B) = 12 \\ &\text{Pencil cases } (P) = 5 \\ &\text{Water bottles } (W) = 7 \end{aligned}$$

\]

Apply the multiplication rule

\[

$$\begin{aligned} \text{Total Sets} &= B \times P \times W \\ &= 12 \times 5 \times 7 \\ &= 60 \times 7 \\ &= 420 \end{aligned}$$

\]
</reasoning>

<answer>
A student can choose from 12 types of backpacks, 5 pencil cases and 7 water bottles. How many school supply sets can they create?

Number of Sets = <blank>420</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Statistics",
"Fundamental Counting Principle"
]
}
</post_analysis>