Yes, your calculation is correct! The binomial coefficient $\binom{7}{2}$ is computed as follows:

$\binom{7}{2} = \frac{7 \times 6}{2} = \frac{42}{2} = 21$

The binomial coefficient $\binom{n}{k}$ represents the number of ways to choose $k$ elements from a set of $n$ elements, and it is calculated using the formula:

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

For $\binom{7}{2}$, the simplified form works out to 21 as you've shown.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this topic:

1. What is the value of $\binom{8}{3}$?
2. How does $\binom{n}{k}$ relate to Pascal's Triangle?
3. Can you explain the symmetry property $\binom{n}{k} = \binom{n}{n-k}$?
4. How does the binomial theorem use binomial coefficients?
5. What is the connection between binomial coefficients and combinations in probability?

Tip: In combinatorics, $\binom{n}{k}$ is often referred to as "n choose k," which represents choosing $k$ items from a group of $n$ without regard to order.