# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/14

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Problem 14

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## Exercise 14

### Question

export const metadata = {
  title: "Problem 14",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

A box contains <InlineMath math="5" /> red balls, <InlineMath math="4" /> white balls, and <InlineMath math="3" /> yellow balls. From the box, <InlineMath math="3" /> balls are drawn simultaneously at random. The probability of drawing <InlineMath math="2" /> red balls and <InlineMath math="1" /> white ball is...


### Choices

- [ ] $$\frac{1}{11}$$
- [x] $$\frac{2}{11}$$
- [ ] $$\frac{4}{11}$$
- [ ] $$\frac{3}{5}$$
- [ ] $$\frac{5}{7}$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 14",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

The number of ways to choose red balls is:

<BlockMath math="C(5,2) = \frac{5!}{2!3!} = 10" />

The number of ways to choose white balls is:

<BlockMath math="C(4,1) = \frac{4!}{3!1!} = 4" />

The total number of possible ways to choose the balls is:

<BlockMath math="C(12,3) = \frac{12!}{9!3!} = 220" />

Let <InlineMath math="A =" /> The event of drawing <InlineMath math="2" /> red balls and <InlineMath math="1" /> white ball.

The probability of drawing <InlineMath math="2" /> red balls and <InlineMath math="1" /> white ball is:

<BlockMath math="\begin{aligned} P(A) &= \frac{C(5,2)C(4,1)}{C(12,3)} \\ &= \frac{10 \cdot 4}{220} \\ &= \frac{40}{220} \\ &= \frac{2}{11} \end{aligned}" />


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