Finding the number of elements of a set 
Let $S$ be the set of all integers from $100$ to $999$ which are neither divisible by $3$ nor divisible by $5$. The number of elements in $S$ is

*

*$480$

*$420$

*$360$

*$240$

My answer is coming out as $420$, but in the actual answer-sheet the answer is given as $480$. Why is my answer not correct? Please, someone help.

Length@Complement[Range[100, 999],Union[Range[102, 999, 3], Range[100, 999,5]]]

(*480*)
