Find the value of $2\left(\frac{7!}{3!4!}\right)$
I recognize that the expression inside the parentheses is a binomial coefficient, which counts the number of ways to choose 3 objects out of 7. Alternatively, I can use the formula for the binomial coefficient, which is $\binom{n}{k} = \frac{n!}{k!(n-k)!}$. Either way, I know that $\binom{7}{3} = \frac{7!}{3!4!} = 35$. So the expression is equal to $2(35) = 70$. 