HMMT-Nov 2016 guts, Problem 3

Evaluate $\frac{2016 !^{2}}{2015 ! 2017 !}$. Here $n$ ! denotes $1 \times 2 \times \cdots \times n$.

Solution: $\frac{2016 !^{2}}{2015 ! 2017 !}=\frac{2016 !}{2015 !} 2016 !=\frac{2016}{1} \frac{1}{2017}=\frac{2016}{2017}$ $\fbox{\frac{2016}{2017}}$.

Answer: \frac{2016}{2017}