21st Century!

$\large \displaystyle \left \lfloor \frac{2002!}{2001! + 2000! + \cdots + 2! + 1!} \right \rfloor = \, ?$

Notations :

• $!$ denotes the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .

• $\lfloor \cdot \rfloor$ denotes the floor function .