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The problem presented is to evaluate \( \binom{9}{4} \), which represents the number of ways to choose 4 objects from a set of 9, also known as a combination.

The formula for combinations is:

\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]

In this case, \( n = 9 \) and \( r = 4 \), so the calculation is:

\[
\binom{9}{4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!}
\]

Let me calculate it for you.The value of \( \binom{9}{4} \) is \( 126 \). Therefore, the correct answer is the third option: **126**.

Would you like further details or have any other questions? 

Here are five related questions:
1. How would you calculate \( \binom{10}{3} \)?
2. What is the difference between combinations and permutations?
3. How would the formula change if you were calculating permutations instead of combinations?
4. What is \( \binom{9}{5} \), and how is it related to \( \binom{9}{4} \)?
5. What does the factorial symbol (!) represent in mathematics?

**Tip**: The combination formula is symmetric, meaning \( \binom{n}{r} = \binom{n}{n-r} \).

Learn how to evaluate the combination \(9C_4\) with a detailed step-by-step solution. This problem demonstrates the key concepts of combinatorics and the use of factorials in calculating combinations. Suitable for students in Grades 8-10.

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