https://file.aiquickdraw.com/mathbot/file/1726614190011eyzdqqvo.jpg

The expression in the image appears to be a binomial coefficient, which is typically written as \( \binom{a}{b} \), denoting "a choose b." In this case, it looks like:

\[
\binom{3}{2}
\]

This is interpreted as the number of ways to choose 2 elements from a set of 3, which is calculated using the combination formula:

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

So, for \( \binom{3}{2} \):

\[
\binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3 \times 2 \times 1}{2 \times 1 \times 1} = \frac{6}{2} = 3
\]

Thus, \( \binom{3}{2} = 3 \).

Would you like more details on this topic or any additional clarifications?

Here are five related questions:
1. How does the combination formula differ from the permutation formula?
2. What is the value of \( \binom{5}{3} \)?
3. How do you calculate factorial values like \( 6! \) or \( 7! \)?
4. What is the difference between combinations and arrangements?
5. How would you use combinations to solve a probability problem?

**Tip:** In combinatorics, order does not matter for combinations, but it does for permutations.

What is the value of the binomial coefficient (3 choose 2)?

Learn how to calculate the binomial coefficient (3 choose 2) using the combination formula. Understand key combinatorics concepts, including how to use factorials to solve for the number of ways to choose 2 elements from 3. Suitable for students in Grades 8-10.

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