Question 2
Find the remainder when $$
9 \cdot 99 \cdot 999 \cdot \cdots \cdot \underbrace{99\ldots9}_{\text{999 nines}}
$$ is divided by $1000.$
9 \cdot 99 \cdot 999 \cdot \cdots \cdot \underbrace{99\ldots9}_{\text{999 nines}}
$$ is divided by $1000.$