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.

Solve[{100 <= n <= 999, ! Element[n/3, Integers], ! 
    Element[n/5, Integers]}, n, Integers] // Length

(*  480  *)

