Your equation is correct. Here's a breakdown of the calculation for clarity:

1. The binomial coefficient $\binom{7}{2}$ is defined as: $\binom{7}{2} = \frac{7!}{2!(7-2)!} = \frac{7!}{2!5!}$
2. Simplifying $\frac{7!}{2!5!}$: $\frac{7!}{2!5!} = \frac{7 \times 6 \times 5!}{2! \times 5!} = \frac{7 \times 6}{2!}$
3. Now, calculate $2!$: $2! = 2 \times 1 = 2$
4. The binomial coefficient becomes: $\frac{7 \times 6}{2} = \frac{42}{2} = 21$
5. Finally, you multiply by $2!$ (which is $2$): $21 \times 2 = 42$

Thus, the final result is $42$.

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Here are some related questions for further practice:

1. How would you compute $\binom{8}{3} \times 3!$?
2. What is the value of $\binom{6}{2} \times 2!$?
3. How do you calculate $\binom{n}{r} \times r!$ for any general $n$ and $r$?
4. What is the factorial of 7 and how do you simplify $\frac{7!}{2!(7-2)!}$?
5. How does the binomial coefficient change if you swap $n$ and $r$?

Tip: The binomial coefficient formula $\binom{n}{r} = \frac{n!}{r!(n-r)!}$ counts the number of ways to choose $r$ elements from a set of $n$ elements without regard to order.