Question

$C^{2000}_{2016} - C^{16}_{2016} = ?$

Answer 1

In fine :

$C_{2016}^{2000}-C_{2016}^{16}= \dfrac{2016!}{2000!(2016-2000)!}-\dfrac{2016!}{16!(2016-16)!}=\\=\dfrac{2016!}{2000! \cdot 16!}-\dfrac{2016!}{2000!\cdot 16!}=\boxed{0}$